Rs Aggarwal 2017 Solutions for Class 9 Math Chapter 1 Real Numbers are provided here with simple step-by-step explanations. These solutions for Real Numbers are extremely popular among Class 9 students for Math Real Numbers Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Rs Aggarwal 2017 Book of Class 9 Math Chapter 1 are provided here for you for free. You will also love the ad-free experience on Meritnation’s Rs Aggarwal 2017 Solutions. All Rs Aggarwal 2017 Solutions for class Class 9 Math are prepared by experts and are 100% accurate.

#### Page No 218:

#### Question 1:

Write down the coordinates of each of the points *A*, *B*, *C*, *D*, *E* shown below:

#### Answer:

Draw perpendicular *AL, BM, CN, DP and EQ *on the *X*-axis.

(i) Distance of *A* from the *Y-*axis = *OL* = -6 units

Distance of *A* from the* X-*axis = *AL* = 5 units

Hence, the coordinates of *A* are (-6,5).

(ii) Distance of *B* from the *Y*-axis = *OM* = 5 units

Distance of *B* from the *X-*axis = *BM* = 4 units

Hence, the coordinates of *B* are (5,4).

(iii) Distance of *C* from the *Y-*axis = *ON* = -3 units

Distance of *C* from the *X-*axis = *CN* = 2 units

Hence, the coordinates of *C* are (-3,2).

(iv) Distance of *D* from the *Y-*axis = *OP* = 2 units

Distance of *D* from the *X*-axis = *DP* = -2 units

Hence, the coordinates of *D* are (2,-2).

(v) Distance of *E* from the *Y*-axis = *OL* = -1 units

Distance of *E* from the *X*-axis = *AL* = -4 units

Hence, the coordinates of *E* are (-1,-4).

#### Page No 218:

#### Question 2:

Draw the lines *X*' *OX* and *YOY*' as the coordinate axes on a paper and plot the following points on it.

(i) *P*(7, 4)

(ii) *Q*(−5, 3)

(iii) *R*(−6, −3)

(iv) *S*(3, −7)

(v) *A*(6, 0)

(vi) *B*(0, 9)

(vii) *O*(0, 0)

(viii) *C*(−3, −3)

#### Answer:

Let *X'OX* and *YOY*' be the coordinate axes.

Fix a convenient unit of length and form point *O*, mark equal distances on *OX, OX', OY *and* OY'*. Use the convention of signs.

(i) Starting from *O*, take 7 units on the *x-*axis and then 4 units on the *y*-axis to obtain the point *P*(7,4).

(ii) Starting from *O*, take -5 units on the *x*-axis and then 3 units on the *y-*axis to obtain the point *Q*(-5,3).

(iii) Starting from *O*, take -6 units on the *x*-axis and then -3 units on the *y-*axis to obtain the point *R*(-6,-3).

(iv) Starting from *O*, take 3 units on the *x*-axis and then -7 units on the *y-*axis to obtain the point *S*(3,-7).

(v) Starting from *O*, take 6 units on the *x*-axis to obtain the point *A*(6,0).

(vi) Starting from *O*, take 9 units on the *y-*axis to obtain the point *B*(0,9).

(vii) Same as origin.

(viii) Starting from *O*, take -3 units on the *x*-axis and then -3 units on the *y-*axis to obtain the point *C*(-3,-3).

#### Page No 219:

#### Question 3:

On which axis do the following points lie?

(i) (7, 0)

(ii) (0, −5)

(iii) (0, 1)

(iv) (−, 0)

#### Answer:

(i) In (7,0), ordinate = 0

∴ (7,0) lies on the *x*-axis.

(ii) In (0,-5), abscissa = 0

∴ (0,-5) lies on the *y*-axis.

(iii) In (0,1), abscissa = 0

∴ (0,1) lies on the *y-*axis.

(iv) In (-4,0), ordinate = 0

∴ (-4,0) lies on the *x-*axis.

#### Page No 219:

#### Question 4:

In which quadrant do the given points lie?

(i) (−6, 5)

(ii) (−3, −2)

(iii) (2, −9)

#### Answer:

(i) Points of the type (-,+) lie in the second quadrant.

Hence, the point (-6,5) lies in quadrant II.

(ii) Points of the type (-,-) lie in the third quadrant.

Hence, the point (-3,-2) lies in quadrant III.

(iii) Points of the type (+,-) lie in the fourth quadrant.

Hence, the point (-6,5) lies in quadrant IV.

#### Page No 219:

#### Question 5:

Draw the graph of the equation, *y* = *x* + 1.

#### Answer:

The given equation is *y* = *x* + 1.

Putting *x* = 0, we get *y* = 0 + 1 = 1

Putting *x* = 1, we get *y* = 1 + 1 = 2

Thus, we have the following table:

x |
0 | 1 |

y |
1 | 2 |

On a graph paper, draw the lines

*X'OX*and

*YOY'*as the

*x*-axis and

*y*-axis, respectively.

*A*(0,1) and

*B*(1,2) on the graph paper.

Join

*AB*and extend it on both directions.

Thus, line

*AB*is the required graph of the equation,

*y*=

*x*+ 1.

#### Page No 219:

#### Question 6:

Draw the graph of the equation, *y* = 3*x* + 2.

#### Answer:

*y*= 3

*x*+ 2.

Putting

*x*= 0, we get

*y*= (3 × 0) + 2 = 2.

Putting

*x*= 1, we get

*y*= (3 × 1) + 2 = 5.

Thus, we have the following table:

x |
0 | 1 |

y |
2 | 5 |

On a graph paper, draw the lines

*X'OX*and

*YOY'*as the

*x*-axis and

*y*-axis, respectively.

*A*(0,2) and

*B*(1,5) on the graph paper.

Join

*AB*and extend it on both sides.

Thus, line

*AB*is the required graph of the equation,

*y*= 3

*x*+ 2.

#### Page No 219:

#### Question 7:

Draw the graph of the equation, *y* = 5*x* − 3.

#### Answer:

*y*= 5

*x*- 3.

Putting

*x*= 0, we get

*y*= (5 × 0) - 3 = -3

Putting

*x*= 1, we get

*y*= (5 × 1) - 3 = 2

Thus, we have the following table:

x |
0 | 1 |

y |
-3 | 2 |

On a graph paper, draw the lines

*X'OX*and

*YOY'*as the

*x*-axis and

*y-*axis, respectively.

*A*(0,-3) and

*B*(1,2) on the graph paper.

Join

*AB*and extend it on both sides.

Thus, line

*AB*is the required graph of the equation,

*y*= 5

*x*- 3.

#### Page No 219:

#### Question 8:

Draw the graph of the equation, *y* = 3*x*.

#### Answer:

The given equation is *y* = 3*x*.

Putting *x* = 0, we get *y* = (3 × 0) = 0.

Putting *x* = 1, we get *y* = (3 × 1) = 3

Thus, we have the following table:

x |
0 | 1 |

y |
0 | 3 |

On a graph paper, draw the lines

*X'OX*and

*YOY'*as the

*x*-axis and

*y*-axis, respectively.

*A*(0,0) and

*B*(1,3) on the graph paper.

Join

*AB*and extend it on both sides.

Thus, line

*AB*is the required graph of the equation,

*y*= 3

*x*.

#### Page No 219:

#### Question 9:

Draw the graph of the equation, *y* = −*x*.

#### Answer:

The given equation is *y* = -*x*.

Putting *x* = 0, we get *y* = 0.

Putting *x* = 1, we get *y* = (-1).

Thus, we have the following table:

x |
0 | 1 |

y |
0 | -1 |

On a graph paper, draw the lines

*X'OX*and

*YOY'*as the

*x*-axis and

*y-*axis, respectively.

*A*(0,0) and

*B*(1,-1) on the graph paper.

Join

*AB*and extend it on both sides.

Thus, line

*AB*is the required graph of the equation,

*y*= -

*x*.

#### Page No 219:

#### Question 1:

The point *P*(−5, 3) lies in

(a) quadrant I

(b) quadrant II

(c) quadrant III

(d) quadrant IV

#### Answer:

(b) quadrant II

Points of the type (-, +) lie in the second quadrant.

Hence, (-5,3) lies in quadrant II.

#### Page No 219:

#### Question 2:

The point *Q*(4, −6) lies in

(a) quadrant I

(b) quadrant II

(c) quadrant III

(d) quadrant IV

#### Answer:

(d) quadrant IV

Explanation:

The points of the type (+, -) lie in the fourth quadrant.

Hence, (4,-6) lies in quadrant IV.

#### Page No 219:

#### Question 3:

The point *A*(0, −4) lies

(a) in quadrant II

(b) in quadrant IV

(c) on the *x*-axis

(d) on the *y*-axis

#### Answer:

*y*- axis

Explanation:

As the abscissa of the point

*A*(0,-4) is 0, it lies on the

*y*-axis.

#### Page No 219:

#### Question 4:

The point *B*(8, 0) lies

(a) in quadrant I

(b) in quadrant IV

(c) on the *x*-axis

(d) on the *y*-axis

#### Answer:

(c) on the *x*-axis

Explanation:

As the ordinate of the point *B*(8,0) is 0, it lies on the *x*-axis.

#### Page No 219:

#### Question 5:

The point *C*(−6, 0) lies

(a) in quadrant II

(b) in quadrant III

(c) on the *x*-axis

(d) on the *y*-axis

#### Answer:

*x*-axis

Explanation:

As the ordinate of the point

*C*(-6,0) is 0, it lies on the

*x*-axis.

#### Page No 219:

#### Question 6:

The point at which the two coordinate axes meet is called

(a) the abscissa

(b) the ordinate

(c) the origin

(d) the quadrant

#### Answer:

(c) the origin

Explanation: The point at which two axes meet is called as the origin.

#### Page No 220:

#### Question 7:

If *x* > 0 and *y* < 0, then the point (*x*, *y*) lies in

(a) quadrant I

(b) quadrant II

(c) quadrant III

(d) quadrant IV

#### Answer:

(d) quadrant IV

Explanation:

The points of the type (+,-) lie in fourth quadrant.

Hence, the point (*x*,*y*), where *x *> 0 and *y* <0, lies in quadrant IV.

#### Page No 220:

#### Question 8:

The points (other than the origin) for which the abscissa is equal to the ordinate lie in

(a) quadrant I only

(b) quadrant I and IV

(c) quadrant I and III

(d) quadrant II and IV

#### Answer:

(c) quadrant I and quadrant III

Explanation:

If abscissa = ordinate, there could be two possibilities.

Either both are positive or both are negative. So, a point could be either (+,+), which lie in quadrant I or it could be of the type (-,-), which lie in quadrant III.

Hence, the points (other then the origin) for which the abscissae are equal to the ordinates lie in quadrant I and III.

#### Page No 220:

#### Question 9:

The points in which abscissa and ordinate have different signs will lie in

(a) quadrant I and II

(b) quadrant I and IV

(c) quadrant IV and II

(d) quadrant II only

#### Answer:

(c) quadrant IV and quadrant II

Explanation:

If the abscissa and ordinate have different signs, there could be two possibilities:

Either the abscissa is positive and the ordinate is negative or the abscissa is positive and the ordinate is negative.

So, a point could be either (+,-), which lie in quadrant IV, or it could be of the type (-,+), which lie in quadrant II.

Hence, points whose abscissae and ordinates have different signs lie in quadrants IV and II.

#### Page No 220:

#### Question 10:

The perpendicular distance of the point *A*(7, 5) from *y*-axis is

(a) 7 units

(b) 5 units

(c) 12 units

(d) 2 units

#### Answer:

(a) 7 units

Explanation:

The abscissa is the distance of a point from the* **y*-axis. For point *A*(7,5), the abscissa is 7.

Hence, the perpendicular distance of the point A from *y*-axis is 7 units.

#### Page No 220:

#### Question 11:

A point both of whose coordinates are negative lies in

(a) quadrant I

(b) quadrant II

(c) quadrant III

(d) quadrant IV

#### Answer:

Explanation:

Points of the type (-,-) lie in the third quadrant.

#### Page No 220:

#### Question 12:

Abscissa of a point is positive in

(a) quadrant I only

(b) quadrant II only

(c) quadrant I and II

(d) quadrant I and IV

#### Answer:

(d) quadrant I and IV

Explanation:

If abscissa of a point is positive, then the ordinate could be either positive or negative.

It means that the type of any point can be either (+,+) or (+, -).

Points of the type (+,+) lie in quadrant I, whereas points of the type (+,-) lie in quadrant IV.

#### Page No 220:

#### Question 13:

The coordinates of two points are *A*(3, 4) and *B*(−2, 5) then (abscissa of *A*) − (abscissa of *B*) = ?

(a) 1

(b) −1

(c) 5

(d) −5

#### Answer:

(c) 5

Explanation:

Abscissa of *A* = 3

Abscissa of *B* = -2

Hence, (abscissa of *A*) - (abscissa of *B*) = 3 - (-2) = 5

#### Page No 220:

#### Question 14:

The points *A*(2, −2), *B*(3, −3), *C*(4, −4) and *D*(5, −5) all lie in

(a) quadrant II

(b) quadrant III

(c) quadrant IV

(d) different quadrants

#### Answer:

(c) quadrant IV

Explanation:

For all the given points, the abscissa is positive and the ordinate is negative.

Such points of the type (+,-) lie in quadrant IV.

#### Page No 220:

#### Question 15:

Which of the points *A*(0, 6) *B*(−2, 0), *C*(0, −5), *D*(3, 0) and *E*(1, 2) does not lie on *x*-axis?

(a) *A* and *C*

(b) *B* and *D*

(c) *A*, *C* and *E*

(d) *E* only

#### Answer:

(c) *A,C* and *E*

Explanation:

The ordinate of the points lying on the *x*-axis = 0

So, the points *B* and *D* lie on the *x*-axis. The rest of the points do not lie on the *x-*axis, as their ordinates are not equal to 0.

Thus, the points *A, C *and* E* do not lie on the* x-*axis.

#### Page No 220:

#### Question 16:

The signs of abscissa and ordinate of a point in quadrant II are respectively

(a) (+, −)

(b) (−, +)

(c) (−, −)

(d) (+, +)

#### Answer:

(b) (-, +)

In quadrant II, the sign of the abscissa is negative and the sign of the ordinate is positive.

#### Page No 220:

#### Question 17:

Which of the following points does not lie on the line *y* = 3*x* + 4?

(a) (1, 7)

(b) (2, 0)

(c) (−1, 1)

(d) (4, 12)

#### Answer:

(d) (4,12)

Explanation:

(a) Point (1,7) satisfy the equation *y *= 3*x* + 4. (∵*y* = 3 × 1 + 4 = 7)

(b) Point (2,10) satisfy the equation *y *= 3*x* + 4. (∵*y* = 3 × 2 + 4 = 10)

(c) Point (-1,1) satisfy the equation *y *= 3*x* + 4. (∵*y* = 3 × -1 + 4 = 1)

(d) Point (4,12) does not satisfy the equation *y* = 3*x* + 4. (∵ *y* = 3 × 4 + 4 = 16 ≠ 12)

Hence, the point (4,12) do not lie on the line *y* = 3*x* +4.

#### Page No 220:

#### Question 18:

Which of the following points lies on the line *y* = 2*x* + 3?

(a) (2, 8)

(b) (3, 9)

(c) (4, 12)

(d) (5, 15)

#### Answer:

(b) (3,9)

Explanation:

Point (2,8) does not satisfy the equation *y* = 2*x* + 3. (∵ *y* = 2 × 2 + 8 = 12$\ne $ 8)

Point (3,9) satisfy the equation *y* = 2*x* + 3. (∵ *y *=2 × 3 + 3 = 9)

Point (4,12) does not satisfy the equation *y* = 2*x* + 3. (∵ *y* = 2 × 4 + 3 = 11$\ne $ 12)

Point (5,15) does not satisfy the equation *y* = 2*x* +3. (∵ *y*= 2 × 5 + 3 = 13$\ne $15)

Hence, the point (3,9) lies on the line *y* = 2*x* +3.

#### Page No 220:

#### Question 19:

If *a* < 0 and *b* < 0, then the point *P*(*a*, *b*) lies in

(a) quadrant IV

(b) quadrant II

(c) quadrant III

(d) quadrant I

#### Answer:

(c) quadrant III

Explanation:

Points of the type (-,-) lie in the third quadrant.

Hence, the point *P*(*a*,*b*), where *a* < 0 and* b* < 0, lie in quadrant III.

#### Page No 221:

#### Question 20:

The perpendicular distance of the point *P*(4, 3) from the *y*-axis is

(a) 3 units

(b) 4 units

(c) 5 units

(d) 7 units

#### Answer:

(b) 4 units

Explanation:

The perpendicular distance of the point *P*(4,3) from the *y*-axis is 4 units (the abscissa).

#### Page No 221:

#### Question 21:

The area of the ∆*OAB* with *O*(0, 0), *A*(4, 0) and *B*(0, 6) is

(a) 8 sq units

(b) 12 sq units

(c) 16 sq units

(d) 24 sq units

#### Answer:

(b) 12 sq units

Explanation:

On plotting the points on a graph paper, we get ∆*OAB** *as a right angle triangle, where* OA* = base = 4 units and *OB* = 6 units

∴ Area of ∆*OAB* = ½ ×* OA* × *OB* = ½ × 4 × 6 = 12 sq units

#### Page No 221:

#### Question 22:

The area of the ∆*OPQ* with *O*(0, 0), *P*(1, 0) and *Q*(0, 1) is

(a) 1 sq unit

(b) $\frac{1}{2}\mathrm{sq}\mathrm{unit}$

(c) $\frac{1}{4}\mathrm{sq}\mathrm{unit}$

(d) 2 sq units

#### Answer:

(b) ½ sq unit

Explanation:

On plotting the points on a graph paper, we get ∆*OPQ *as a right angle triangle, where* OP* = base = 1 units and *OQ* = 1 units

∴ Area of (∆*OPQ*) = ½ ×* OP* × *OQ* = ½ × 1 × 1 = ½ sq unit

#### Page No 221:

#### Question 23:

Consider the three statements given below:

I. Any point on *x*-axis is of the form (*a*, 0).

II. Any point on *y*-axis is of the form (0, *b*).

III. The point *P*(3, 3) lies on both the axes.

Which is true?

(a) I and II

(b) I and III

(c) II and III

(d) III only

#### Answer:

(a) I and II

Explanation:

Ordinates of points lying on the *x*-axis = 0

Abscissae of points lying on the *y*-axis = 0

In point *P*(3,3), neither the abscissa nor the ordinate is 0. Hence, statements I and II are true.

#### Page No 221:

#### Question 24:

**Assertion:** The point *P*(−3, 0) lies on *x*-axis.

**Reason:** Every point on *x*-axis is of the form (*x*, 0).

(a) Both Assertion and Reason are true and Reason is a correct explanation of Assertion.

(b) Both Assertion and Reason are true but Reason is not a correct explanation of Assertion.

(c) Assertion is true and Reason is false.

(d) Assertion is false and Reason is true.

#### Answer:

(a) Both Assertion and Reason are true and Reason is a correct explanation of Assertion.

Explanation:

Assertion (A): The point *P*(-3,0) lies on the *x-*axis. This is true, as the ordinate of the point is 0.

Reason (R): Every point on the *x-* axis is of the form (*x*,0). This is also a true statement.

Hence, both the assertion and the reason are true and reason (R) is the correct explanation of assertion (A).

The correct answer is (a).

#### Page No 221:

#### Question 25:

**Assertion:** The point *O*(0, 0) lies in quadrant I.

**Reason:** The point *O*(0, 0) lies on both the axes.

(a) Both Assertion and Reason are true and Reason is a correct explanation of Assertion.

(b) Both Assertion and Reason are true but Reason is not a correct explanation of Assertion.

(c) Assertion is true and Reason is false.

(d) Assertion is false and Reason is true.

#### Answer:

(d) Assertion (A) is false and Reason (R) is true.

Explanation:

Assertion (A): The point *O*(0,0) lies in quadrant I. This is a false statement, as point O is the origin where two axes intersect each other.

Reason (R): The point *O*(0, 0) lies on both the axes. This is a true statement.

Hence, assertion (A) is false and reason (R) is true.

So, the correct answer is (d).

#### Page No 222:

#### Question 26:

**Assertion:** The point* P*(−6, −4) lies in quadrant III.

**Reason:** The signs of points in quadrants I, II, III and IV are respectively (+, +), (−, +), (−, −) and (+, −).

(a) Both Assertion and Reason are true and Reason is a correct explanation of Assertion.

(b) Both Assertion and Reason are true but Reason is not a correct explanation of Assertion.

(c) Assertion is true and Reason is false.

(d) Assertion is false and Reason is true.

#### Answer:

(a) Both Assertion and Reason are true and Reason is a correct explanation of Assertion.

Explanation:

Assertion (A): The point *P*(-6,-4) lies in quadrant III. This is a true statement, as points of the type (-,-) lie in quadrant III.

Reason (R): The signs of the points in quadrants I, II, III and IV are (+, +), (−,+), (−,−) and (+,−), respectively. This is also a true statement.

Clearly, reason ( R) justifies assertion (A), as those points of the type (-,-) lie in quadrant III.

Hence, (a).

#### Page No 222:

#### Question 27:

**Assertion:** If *a* ≠ *b*, then (*a*, *b*) ≠ (*b*, a).

**Reason:** (4, −3) lies in quadrant IV.

(a) Both Assertion and Reason are true and Reason is a correct explanation of Assertion.

(b) Both Assertion and Reason are true but Reason is not a correct explanation of Assertion.

(c) Assertion is true and Reason is false.

(d) Assertion is false and Reason is true.

#### Answer:

(b) Both Assertion and Reason are true but Reason is not a correct explanation of Assertion.

Explanation:

Assertion (A): If *a* ≠ *b*, then (*a*, *b*) ≠ (*b*, a), which is a true statement.

Reason ( R ): (4, −3) lies in quadrant IV, as points of the type (+,-) lie in the fourth quadrant. So, the reason (R) is also a true statement.

But, the reason does not justify the assertion.

Hence, the correct answer is (b).

#### Page No 222:

#### Question 28:

Write whether the following statements are true or false?

(i) The point *P*(6, 0) lies in the quadrant I.

(ii) The perpendicular distance of the point *A*(5, 4) for *x*-axis is 5 units.

#### Answer:

(i) False

Explanation:

The ordinate of the point *P*(6,0) is 0. So, it lies on the *x-*axis.

(ii) False

Explanation:

The perpendicular distance of the point A( 5,4) from* *the* x-*axis will be 4 units, not 5 units.

#### Page No 222:

#### Question 29:

State whether true or false:

(i) The mirror image of the pint *A*(4, 5) in the *x*-axis is *A*'(−4, 5).

(ii) The mirror image of the pint *A*(4, 5) in the *y*-axis is *A*'(−4, 5).

#### Answer:

(i) False

Explanation:

The mirror image of the point *A*(4,5) on the *x-*axis is *A*'(4,-5), not *A*'(-4,5).

(ii) True

Explanation:

The mirror image of the point *A*(4,5) on the *y-*axis is *A'*(-4,5).

#### Page No 222:

#### Question 30:

Write whether the following statements are true or false:

(a) The point (−5, 0) lies on *x*-axis.

(b) The point (0, −3) lies in quadrant II.

#### Answer:

(i)True

Explanation:

The point (−5,0) lies on the *x*-axis, as any point whose ordinate is 0 lies on the* x-*axis .Therefore, the given statement is correct.

(ii) False

Explanation:

The point (0,-3) lies on the *y*-axis. So, the given statement is false.

#### Page No 222:

#### Question 31:

Match the following columns:

Column I |
Column II |

(a) Equation of x-axis is |
(p) (a, 0) |

(b) Equation of y-axis is |
(q) y = 0 |

(c) Any point on x-axis is of the form |
(r) (0, b) |

(d) Any point on y-axis is of the form |
(s) x = 0 |

(b) ......,

(c) ......,

(d) ......,

#### Answer:

(a)-(q), (b)-(s), (c)-(p) and (d)-(r)

Explanation:

(a) As the points that lie on the x-axis have their ordinates equal to 0, the equation of the x-axis will be *y* = 0.

(b) As the points that lie on the *y*-axis have their absiccae equal to 0, the equation of the *y*-axis will be *x *= 0.

(c) Any point on the *x*-axis is of the form (*a*,0).

(d) Any point on the *y*-axis is of the form (0,*b*).

#### Page No 223:

#### Question 32:

Match the following columns:

Column I |
Column II |

(a) The point A(−3, 0) lies on |
(p) y-axis |

(b) The point B(−5, −1) lies in quadrant |
(q) IV |

(c) The point C(2, −3) lies in quadrant |
(r) III |

(d) The point D(0, −6) lies on |
(s) x-axis |

(b) ......,

(c) ......,

(d) ......,

#### Answer:

(a)-(s), (b)-(r), (c)-(q) and (d)-(p)

Explanation:

The points of the type (*a,*0) lie on the *x*-axis.

The points of the type (-,-) lie in quadrant III.

The points of the type (+,-) lie in quadrant IV.

The points of the type (0,*b*) lie on the *y*-axis.

#### Page No 223:

#### Question 33:

Without plotting the given points on a graph paper indicate the quadrants in which they lie, it

(a) ordinate = 6, abscissa = −3

(b) ordinate = −6, abscissa = 4

(c) abscissa = −5, ordinate = −7

(d) ordinate = 3, abscissa = 5

#### Answer:

(a) Point (-3,6) lie in quadrant II.

(b) Point (4,-6) lie in quadrant IV.

(c) Point (-5,-7) lie in quadrant III.

(d) Point (5,3) lie in quadrant I.

#### Page No 223:

#### Question 34:

Plot the point *P*(−6, 3) on a graph paper. Draw *PL* ⊥ *x*-axis and PM ⊥ *y*-axis. Write the coordinates of *L* and *M*.

#### Answer:

The required point is shown in the graph given above.

Also, draw *PL *⊥ *x*-axis and *PM* ⊥ *y*-axis.

The coordinates of *L* and *M *are (-6,0) and(0,3), respectively.

#### Page No 223:

#### Question 35:

Plot the points *A*(−5,2), *B*(3,−2), *C*(−4,−3) and *D*(6, 0) on a graph paper.

#### Answer:

The points *A*(-5,2), *B*(3,-2), *C*(-4,-3) and *D*(6,0) are plotted on the graph paper.

#### Page No 223:

#### Question 36:

The three vertices of ∆*A**BC* are *A*(1, 4), *B*(−2, 2) and *C*(3, 2). Plot these points on a graph paper and calculate the area of ∆*ABC*.

#### Answer:

Let *A*(1,4), *B*(-2,2) and *C*(3,2) be the vertices of ∆*ABC**.*

On plotting the points on the graph paper and joining the points, we get ∆*ABC** *as shown above.

Let *BC* intersect *y*-axis at *D*.

Then* BC* = *BD + DC* = (2 + 3) units = 5 units ( Abscissa of *B* = -2, which indicates that it is on the left side of *y*-axis. So, for calculating the length of* BC*, we will consider only the magnitude)

Draw *AM* ⊥ *x* -axis meeting *BC* at* L.*

Ordinate of point *L* = ordinate of point *C* = 2

So, *AL* = *AM - LM* = (4 - 2) units = 2 units

∴ Area of (∆*ABC*) = ½ ×* BC* × *AL* = ½ × 5 × 2 = 5 sq units

#### Page No 223:

#### Question 37:

The three vertices of a rectangle *ABCD* are *A*(2, 2) *B*(−3, 2) and *C*(−3, 5). Plot these points on a graph paper and find the coordinates of *D*. Also, find the area of rectangle *ABCD*.

#### Answer:

Let

*A*(2,2),

*B*(-3,2) and

*C*(-3,5) be the three vertices of rectangle

*ABCD.*

On plotting the points on the graph paper and joining the points, we see that points

*B*and

*C*lie on quadrant II and point

*A*lies on quadrant I

*.*

Let

*D*be the fourth vertex of the rectangle.

So, abscissa of

*D*= abscissa of

*A*= 2

Also, ordinate of

*D*= ordinate of

*C*= 5

So, coordinates of point

*D*= (2,5)

Let the

*y*-axis cut

*AB*and

*CD*at points

*L*and

*M*, respectively.

Now,

*AB*= (

*BL*+

*LA*) = (3 + 2) units = 5 units (Abscissa of

*B*= -3, which indicates that it is on the left side of

*y*-axis. So, for calculating the length of

*AB*, we will consider only the magnitude.)

Thus,

*BC*= (5 - 2) units = 3 units

∴ Area of rectangle

*ABCD*=

*BC*×

*AB*= 3 × 5 = 15 sq units

#### Page No 223:

#### Question 38:

The three vertices of a square *ABCD* are *A*(3, 2) *B*(−2, 2) and *D*(3, −3). Plot these points on a graph paper and hence, find the coordinates of *C*. Also, find the area of square *ABCD*.

#### Answer:

Let *A*(3,2), *B*(-2,2) and *D*(3,-3) be the three vertices of square *ABCD*.

On plotting the points on the graph paper and joining the points, we see that *A, B* and *D* lie in different quadrants.

Let *C* be the fourth vertex of the square.

∴ Abscissa of *C* = abscissa of *B* = -2

Also, ordinate of *C* = ordinate of *D* = -3

So, coordinates of *D* = (-2,-3)

Let the *y*-axis cut* AB* and *CD* at points* L* and *M*, respectively.

Now, *AB *= (*BL* + *LA*) = (2 + 3) units = 5 units (Abscissa of *B* = -2, which indicates that it is on the left side of *y*-axis. So, for calculating the length of *AB*, we will consider only the magnitude.)

∴ Area of *ABCD* = *AB* × *AB* = 5 × 5 = 25 sq units

#### Page No 224:

#### Question 39:

From the figure given below write each of the following:

(i) The coordinates of point *D*

(ii) The abscissa of the point *A*

(iii) The point whose coordinates are (2, −3)

(iv) The point whose coordinates are (−3, −4)

(v) The ordinate of point *E*

(vi) The coordinates of *B*

(vii) The coordinates of *F*

(viii) The coordinates of the origin

#### Answer:

(i) As the abscissa of point *D* is 0 and the ordinate is -5, the coordinates of point *D* are (0,-5).

(ii) The abscissa of point *A* is -4.

(iii) The coordinates of point *E* are (2,-3).

*C*are (-3,-4).

(v) Ordinate of point

*E*= -3

(vi) The point

*B*lies on the

*x-*axis, i.e., abscissa = -2 and ordinate = 0.

So, the coordinates of

*B*are (-2,0).

(vii) Abscissa of point

*F*= 5 and ordinate = -1

So, coordinates of point

*F*are (5,-1).

#### Page No 228:

#### Question 1:

If *x* < 0 and *y* > 0, then the point (*x*, *y*) lies in

(a) quadrant I

(b) quadrant II

(c) quadrant III

(d) quadrant IV

#### Answer:

(b) quadrant II

Explanation:

Those points of the type (-,+) lie on the second quadrant. Hence, if *x* < 0 and *y* > 0, then the point (*x*, *y*) lies in quadrant II.

#### Page No 228:

#### Question 2:

Which point does not lie in any quadrant?

(a) (3, −6)

(b) (−3, 4)

(c) (5, 7)

(d) (0, 3)

#### Answer:

(d) (0,3)

Explanation:

The point (0,3) lies on the *y-*axis.

#### Page No 229:

#### Question 3:

The area of ∆*AOB* having vertices *A*(0, 6), *O*(0, 0) and *B*(6, 0) is

(a) 12 sq units

(b) 36 sq units

(c) 18 sq units

(d) 24 sq units

#### Answer:

(c) 18 sq units

Explanation:

On plotting the points on the graph paper, we get the right angle ∆*AOB,* where* OB* = base = 6 units and height = *OA* = 6 units

∴ Area of ∆*AOB* = $\frac{1}{2}$ ×* OA* × *OB* = $\frac{1}{2}$ × 6 × 6 = 18 sq units

#### Page No 229:

#### Question 4:

Read the statements given below and choose the correct answer:

I. Any point on *x*-axis is of the form (*x*, 0) for all *x*.

II. Any point on *y*-axis is of the form (0, *y*) for all *y*.

III. Any point on both the axes is of the form (*x*, *y*) for all *x* and *y*.

Which of the following is true?

(a) I and II

(b) I and III

(c) I only

(d) III only

#### Answer:

(a) I and II

The correct statements are:

I: Any point on the *x*-axis is of the form (*x*,0) for all *x*.

II. Any point on the *y*-axis is of the form (0, *y*) for all *y*.

#### Page No 229:

#### Question 5:

Which of the following points does not lie on the line 3*y* = 2*x* − 5?

(a) (7, 3)

(b) (1, −1)

(c) (−2, −3)

(d) (−5, 5)

#### Answer:

Explanation:

(-5,5) does not satisfy the equation 3

*y*= 2

*x*- 5

[RHS = 2 x (-5) - 5 = -15; LHS = 3 x 5 = 15 and 15 ≠ (-15)]

So, the point (-5,5) does not lie on the equation.

#### Page No 229:

#### Question 6:

Plot each of the following points on a graph paper:

*A*(3, −5), *B*(−5, −2), *C*(−6, 1) and *D*(4, 0).

#### Answer:

The points *A*(3,-5), *B*(-5,-2), *C*(-6,1) and *D*(4,0) are plotted on the graph paper.

#### Page No 229:

#### Question 7:

If 2*y* = 3 − 5*x*, find the value of *y* when *x* = −1.

#### Answer:

On putting the value of *x* = -1 in the equation, 2*y* = 3 - 5*x**, *we get:

2*y* = 3 - 5 × (-1)

⇒* y =* $\frac{1}{2}$ × [3 - 5 × (-1)] = 4

∴* y* = 4 when *x* = -1

#### Page No 229:

#### Question 8:

On which axis does the point *A*(0, −4) lie?

#### Answer:

*A*(0,-4) = 0

Hence,

*A*lies on the

*y*-axis.

#### Page No 229:

#### Question 9:

In which quadrant does the point *B*(−3, −5) lie?

#### Answer:

*B*(-3,-5)

*are negative and those points of the type (-,-) lie in the third quadrant.*

Hence, point

*B*lies in quadrant III.

#### Page No 229:

#### Question 10:

What is the perpendicular distance of the point *P*(−2, −3) from the *y*-axis?

#### Answer:

Abscissa of point *P*(-2,-3) = -2

*P*(-2,-3) from the

*y*-axis is 2 units.

#### Page No 229:

#### Question 11:

At what point do the coordinate axes meet?

#### Answer:

The coordinate axes (*x*-axis and *y-*axis) meet at point *O*(0,0), known as the origin.

#### Page No 229:

#### Question 12:

For each of the following write true or false

(i) The point (4, 0) lies in quadrant I.

(ii) The ordinate of a point *P* is −3 and its abscissa is −4. The point is *P*(−3, −4).

(iii) The points *A*(1, −1) and *B*(−1, 1) both lies in quadrant IV.

(iv) A point lies on *y*-axis at a distance of 3 units from *x*-axis. Its coordinates are (3, 0).

(v) The point *C*(0, −5) lies on *y*-axis.

(vi) The point *O*(0, 0) lies on *x*-axis as well as *y*-axis.

#### Answer:

(i) False. It lies on the *x*-axis.

(ii) False. The point is *P*(-4,-3).

(iii) False. *A*(1,-1) lies in quadrant IV and *B* (-1,1) lies in quadrant II.

(iv) False. The coordinates of the point are (0,3).

(v) True.

(vi) True.

#### Page No 229:

#### Question 13:

Taking a suitable scale, plot the following points on a graph paper:

x |
−4 | −2 | 5 | 0 | 3 | −5 |

y |
6 | −7 | 5 | −1 | −6 | 0 |

#### Answer:

The points

*A*(-4, 6),

*B*( -2,-7),

*C*( 5,5),

*D*(0,-1),

*E*( 3, -6) and

*F*(-5,0) are plotted on the graph paper.

#### Page No 230:

#### Question 14:

Read the graph paper given below and answer the following:

(i) Write the points whose ordinate is 0.

(ii) Write the points whose abscissa is 0.

(iii) Write the points whose ordinate is −3.

(iv) Write the points whose abscissa is 2.

(v) Write the coordinates of all points in quadrant II.

(vi) Write the coordinates of all those points for which abscissa and ordinate have the same value.

#### Answer:

(i) The points *G*(-3,0), *H*(-8,0)*,** Q*(4,0)and *R*(9,0*)* lie on the *x-*axis. Hence, their ordinates are equal to 0.

(ii) The points *L*(0,-6)*, K*(0,-2), *D*(0,3)* *and *C*(0,7) lie on the *y-*axis. Hence, their abscissae are equal to 0.

(iii) The ordinates of points *M*(1,-3), *J*(-4,-3) and *P*(6,-3) are equal to -3.

(iv) *B*(2,4) and *N* 2,-1)

(v) The points *E* and *F* lie in quadrant II.

Coordinates of *E* = (-4,4)

Coordinates of *F* = (-6,2)

(vi) *A*( 3,3) and *I*(-2,-2)

#### Page No 230:

#### Question 15:

(i) Write the mirror image of the point (2, 5) in the *x*-axis.

(ii) Write the mirror image of the point (3, 6) in the *y*-axis.

(iii) A point (*a*, *b*) lies in quadrant II. In which quadrant does (*b*, *a*) lie?

#### Answer:

(i) The mirror image of the point (2,5) in the *x*-axis is (2,*−*5).

(ii) The mirror image of the point (3,6) in the *y*-axis is (*−*3,6).

(iii) If a point (*a,b*) lies in quadrant II, then *a* must be a negative number and *b* must be a positive number. So, the point (*b,a*) or (+,*−*) lie in quadrant IV.

#### Page No 230:

#### Question 16:

Without plotting the points on a graph paper indicate the quadrant in which they lie:

(i) ordinate = 4, abscissa = −3

(ii) ordinate = −5, abscissa = 4

(iii) abscissa = −1, ordinate = −2

(iv) abscissa = −5, ordinate = 3

(v) abscissa = 2, ordinate = 1

(vi) abscissa = 7, ordinate = −4

#### Answer:

(i) Point (*−*3,4) lies in quadrant II.

(ii) Point (4,*−*5) lies in quadrant IV.

(iii) Point (*−*1,*−*2) lies in quadrant III.

(iv) Point (*−*5, 3) lies in quadrant II.

(v) Point (2,1) lies in quadrant I.

(vi) Point (7,*−*4) lies in quadrant IV.

#### Page No 231:

#### Question 17:

Which of the following points do not lie on *x*-axis?

(i) *A*(0, 6)

(ii) *B*(2, 0)

(iii) *C*(0, −2)

(iv) *D*(−6, 0)

(v) *E*(2, 1)

(vi) *F*(0, 4)

#### Answer:

The points *B*(2,0) and *D*(*−*6,0) have their ordinates equal to 0. Hence, they lie on the *x*-axis.

The rest of the points whose ordinate is not equal to zero (i.e., *A, C, E* and *F*) do not lie on the *x*-axis.

Hence, the points *A, C, E* and *F* do not lie on the *x*-axis.

#### Page No 231:

#### Question 18:

Three vertices of a rectangle *ABCD* are *A*(3, 1), *B*(−3, 1) and *C*(−3, 3). Plot these points on a graph paper and find the coordinates of the fourth vertex *D*.

#### Answer:

Let *A*( 3,1), *B*(-3,1) and *C*(-3,3) be the three vertices of rectangle *ABCD.*

On plotting the points on a graph paper and joining the points, we see that *A* lie in quadrant I and *B* and *C* lie in quadrant II.

Let *D* be the fourth vertex of the rectangle.

i.e., Abscissa of *D* = abscissa of *A* = 3

Also, ordinate of *D* = ordinate of *C* = 3

∴ Coordinates of the fourth vertex, *D* = (3,3)

#### Page No 231:

#### Question 19:

Write the coordinates of vertices of a rectangle *OABC*, where *O* is the origin, length *OA* = 5 units lying along *x*-axis, breadth *AB* = 3 units and *B* lying in the fourth quadrant.

#### Answer:

**Given:** *OABC* is a rectangle. *O* is the origin, *OA* = 5 units along the *x*-axis, *AB* = 3 units and *B* lies in quadrant IV.

**Solution: **Coordinates of origin, i.e., *O* = (0,0)

Point *A* lies on the *x*-axis. So, coordinates of point *A* = (5,0)

Point *B* lies in the fourth quadrant. So, ordinate of point *B* is negative.

As width *AB* = 3 units, coordinates of point *B* = ( 5,−3)

Point *C* and point *O* lies on the same line.

Hence, abscissa of *C* = abscissa of *O* = 0

It means that point *C* lies on the *y*-axis.

Similarly, point *C* and point *B* lie on the same altitude. So, the ordinates of both points must be equal.

i.e., ordinate of *C* = ordinate of *B* = (−3)

i.e., coordinates of *C* = (0, *−*3)

Thus, the coordinates of the vertices of rectangle* OABC* are *O*(0,0), *A*( 5,0),* B*( 5, -3) and *C*( 0,-3).

#### Page No 231:

#### Question 20:

Plot the points *A*(2, 5), *B*(−2, 2) and *C*(4, 2) on a graph paper. Join *AB*, *BC* and *AC*. Calculate the area of ∆*ABC*.

#### Answer:

Let *A*( 2,5), *B*(-2,2) and *C*(4,2) be the three vertices of ∆*ABC.*

On plotting the points on a graph paper and joining the points, we see that points *A* and *C* lie in quadrant I and point B lie in quadrant II.

Let *BC* intersects *y*-axis at point *D*.

*BC *= (*BD* + *DC*) = (2 + 4) units = 6 units (Abscissa of *B* = −2, which indicates that it is on the left side of *y*-axis. So, for calculating the length of *BC*, we will consider the magnitude only)

Draw *AM* ⊥* x*-axis and intersect *BC* at *L*.

Ordinate of point L = ordinate of point B = ordinate of point C

*AL = AM − LM* = (5 *−* 2) units = 3 units

∴ Area of ∆*ABC* = ½ × *BC* × *AL* = ½ × 6 × 3 = 9 sq units

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