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#### Page No 174:

#### Question 1:

On the plane of a graph paper draw *X'OX* and *YOY'* as coordinate axes and plot each of the following points.

(i) *A*(5, 3)

(ii) *B*(6, 2)

(iii) *C*(–5, 3)

(iv) *D*(4, –6)

(v) *E*(–3, –2)

(vi) *F*(–4, 4)

(vii) *G*(3, –4)

(viii) *H*(5, 0)

(ix) *I*(0, 6)

(x) *J*(–3, 0)

(xi) *K*(0, –2)

(xii) *O*(0, 0)

#### Answer:

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

(ix)

(x)

(xi)

(xii)

#### Page No 175:

#### Question 2:

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 175:

#### Question 3:

For each of the following points, write the quadrant in which it lies

(i) (–6, 3)

(ii) (–5, –3)

(iii)* *(11, 6)

(iv) (1, –4)

(v) (–7, –4)

(vi) (4, –1)

(vii) (–3, 8)

(viii) (3, –8)

#### Answer:

(i) (–6, 3)

Points of the type (–, +) lie in the II quadrant.

Hence, the point lies (–6, 3) in the II quadrant.

(ii) (–5, –3)

Points of the type (–, –) lie in the III quadrant.

Hence, the point lies (–5, –3) in the III quadrant.

(iii)* *(11, 6)

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

Hence, the point lies (11, 6) in the I quadrant.

(iv) (1, –4)

Points of the type (+, –) lie in the IV quadrant.

Hence, the point lies (1, –4) in the IV quadrant.

(v) (–7, –4)

Points of the type (–, –) lie in the III quadrant.

Hence, the point lies (–7, –4) in the III quadrant.

(vi) (4, –1)

Points of the type (+, –) lie in the IV quadrant.

Hence, the point lies (4, –1) in the IV quadrant.

(vii) (–3, 8)

Points of the type (–, +) lie in the II quadrant.

Hence, the point lies (–3, 8) in the II quadrant.

(viii) (3, –8)

Points of the type (+, –) lie in the IV quadrant.

Hence, the point lies (3, –8) in the IV quadrant.

#### Page No 175:

#### Question 4:

Write the axis on which the given point lies.

(i) (2, 0)

(ii) (0, –5)

(iii) (–4, 0)

(iv) (0, –1)

#### Answer:

(i) (2, 0)

The ordinate of the point (2, 0) is zero.

Hence, the (2, 0) lies on the *x*-axis.

(ii) (0, –5)

The abscissa of the point (0, –5) is zero.

Hence, the (0, –5) lies on the *y*-axis.

(iii) (–4, 0)

The ordinate of the point (–4, 0) is zero.

Hence, the (–4, 0) lies on the *x*-axis.

(iv) (0, –1)

The abscissa of the point (0, –1) is zero.

Hence, the (0, –1) lies on the *y*-axis.

#### Page No 175:

#### Question 5:

Which of the following points lie on the *x*-axis?

(i) *A*(0, 8)

(ii) *B*(4, 0)

(iii) *C*(0, –3)

(iv) *D*(–6, 0)

(v) *E*(2, 1)

(vi) *F*(–2, –1)

(vii) *G*(–1, 0)

(viii) *H*(0, –2)

#### Answer:

(i) *A*(0, 8)

The given point does not lies on the *x*-axis.

(ii) *B*(4, 0)

The ordinate of the point (4, 0) is zero.

Hence, the (4, 0) lies on the *x*-axis.

(iii) *C*(0, –3)

The given point does not lies on the *x*-axis.

(iv) *D*(–6, 0)

The ordinate of the point (–6, 0) is zero.

Hence, the (–6, 0) lies on the *x*-axis.

(v) *E*(2, 1)

The given point does not lies on the *x*-axis.

(vi) *F*(–2, –1)

The given point does not lies on the *x*-axis.

(vii) *G*(–1, 0)

The ordinate of the point (–1, 0) is zero.

Hence, the (–1, 0) lies on the *x*-axis.

(viii) *H*(0, –2)

The given point does not lies on the *x*-axis.

#### Page No 175:

#### Question 6:

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:

Abscissa of *D* = Abscissa of *A* = 2

Ordinate of *D* = Ordinate of *B* = 2

Now,

BC = (2 + 4) units = 6 units

AD = (5 – 2) units = 3 units

$\mathrm{Area}\mathrm{of}\u2206ABC=\frac{1}{2}\times \mathrm{Base}\times \mathrm{Height}\phantom{\rule{0ex}{0ex}}=\frac{{\displaystyle 1}}{{\displaystyle 2}}\times BC\times AD\phantom{\rule{0ex}{0ex}}=\frac{1}{2}\times 6\times 3\phantom{\rule{0ex}{0ex}}=9$

Hence, area of ∆*ABC *is 9 square units.

#### Page No 175:

#### Question 7:

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*. Also, find the area of rectangle *ABCD*.

#### Answer:

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

Let the *y*-axis cut the rectangle *ABCD* at the points *P* and *Q *respectively.

Abscissa of *D* = Abscissa of *A* = 3.

Ordinate of *D* = Ordinate of *C* = 3.

∴ coordinates of *D* are (3, 3).

*AB* = (*BP* + *PA*) = (3 + 3) units = 6 units.

*BC* = (*OQ* – *OP*) = (3 – 1) units = 2 units.

Ar(rectangle *ABCD*) = (*AB* × *BC*)

= (6 × 2) sq. units

= 12 sq. units

Hence, the area of rectangle *ABCD* is 12 square units.

#### Page No 176:

#### Question 1:

In which quadrant does the point (–7, –4) lie?

(a) IV

(b) II

(c) III

(d) None of these

#### Answer:

Points of the type (–, –) lie in the III quadrant.

The point (–7, –4) lies in the III quadrant.

Hence, the correct option is (c).

#### Page No 176:

#### Question 2:

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 176:

#### Question 3:

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 176:

#### Question 4:

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 176:

#### Question 5:

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 176:

#### Question 6:

The points (–5, 3) and (3, –5) lie in the

(a) same quadrant

(b) II and III quadrants respectively

(c) II and IV quadrants respectively

(d) IV and II quadrants respectively

#### Answer:

The point (–5, 3) lies in the II quadrant.

The point (3, –5) lies in the IV quadrant.

Hence, the correct option is (c).

#### Page No 176:

#### Question 7:

Points (1, –1), (2, –2), (–3, –4), (4, –5)

(a) all lie in the II quadrant

(b) all lie in the III quadrant

(c) all lie in the IV quadrant

(d) do not lie in the same quadrant

#### Answer:

The point (1, –1) lies in the IV quadrant.

The point (2, –2) lies in the IV quadrant.

The point (–3, –4) lies in the III quadrant.

The point (4, –5) lies in the IV quadrant.

Hence, the correct option is (d).

#### Page No 176:

#### Question 8:

Point (0, –8) lies

(a) in the II quadrant

(b) in the IV quadrant

(c) on the *x-*axis

(d) on the *y-*axis

#### Answer:

The abscissa of the point (0, –8) is zero.

The point (0, –8) lies on the *y*-axis.

Hence, the correct option is (d).

#### Page No 176:

#### Question 9:

Point (–7, 0) lies

(a) on the negative direction of the *x*-axis

(b) on the negative direction of the *y*-axis

(c) in the III quadrant

(d) in the IV quadrant

#### Answer:

The point (–7, 0) lies on the negative direction of the *x*-axis.

Hence, the correct option is (a).

#### Page No 177:

#### Question 10:

The point which lies on the *y*-axis at a distance of 5 units in the negative direction of the *y*-axis is

(a) (–5, 0)

(b) (0, –5)

(c) (5, 0)

(d) (0, 5)

#### Answer:

The point which lies on the *y*-axis at a distance of 5 units in the negative direction of the *y*-axis is (0, –5).

Hence, the correct option is (b).

#### Page No 177:

#### Question 11:

The ordinate of every point on the *x*-axis is

(a) 1

(b) –1

(c) 0

(d) any real number

#### Answer:

The ordinate of every point on the *x*-axis is 0.

Hence, the correct option is (c).

#### Page No 177:

#### Question 12:

If the *y*-coordinate of a point is zero then this point always lies

(a) on the *y*-axis

(b) on the *x*-axis

(c) in the I quadrant

(d) in the IV quadrant

#### Answer:

The coordinates of a point on the *x*-axis are of the form (*x*, 0) and that of the point on the *y*-axis is of the form (0, *y*).

Thus, if the *y*-coordinate of a point is zero, then this point always lies on the *x*-axis.

Hence, the correct answer is option (b).

#### Page No 177:

#### Question 13:

If *O*(0, 0), *A*(3, 0), *B*(3, 4), *C*(0, 4) are four given points then the figure *OABC *is a

(a) square

(b) rectangle

(c) trapezium

(d) rhombus

#### Answer:

The point O(0, 0) is the origin.

A(3, 0) lies on the positive direction of *x*-axis.

B(3, 4) lies in the Ist quadrant.

C(0, 4) lies on the positive direction of *y-*axis.

The points O(0, 0), A(3, 0), B(3, 4) and C(0, 4) can be plotted on the Cartesian plane as follows:

Here, the figure OABC is a rectangle.

Hence, the correct answer is option (b).

#### Page No 177:

#### Question 14:

If *A*(–2, 3) and *B*(–3, 5) are two given points then (abscissa of *A*) – (abscissa of *B*) = ?

(a) –2

(b) 1

(c) –1

(d) 2

#### Answer:

The given points are A(–2, 3) and B(–3, 5).

Abscissa of A = *x*-coordinate of A = –2

Abscissa of B = *x*-coordinate of B = –3

∴ Abscissa of A – Abscissa of B = –2 – (–3) = –2 + 3 = 1

Hence, the correct answer is option (b).

#### Page No 177:

#### Question 15:

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

(a) 3

(b) 4

(c) 5

(d) 7

#### Answer:

The perpendicular distance of a point from the *y*-axis is equal to the *x*-coordinate of the point.

∴ Perpendicular distance of the point A(3, 4) from the *y*-axis = *x*-coordinate of A(3, 4) = 3

Hence, the correct answer is option (a).

#### Page No 177:

#### Question 16:

Abscissa of a point is positive in

(a) I and II quadrants

(b) I and IV quadrants

(c) I quadrant only

(d) II quadrant only

#### Answer:

(b) I and IV quadrants

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 177:

#### 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 177:

#### Question 18:

The point whose ordinate is 3 and which lies on the *y*-axis is

(a) (3, 0)

(b) (0, 3)

(c) (3, 3)

(d) (1, 3)

#### Answer:

The ordinate of a point is the *y*-coordinate of the point. So, the *y*-coordinate of the point is 3.

Also, any point on the *y*-axis has coordinates in the form (0, *y*).

Thus, the point whose ordinate is 3 and which lies on the *y*-axis is (0, 3).

Hence, the correct answer is option (b).

#### Page No 177:

#### Question 19:

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 177:

#### Question 20:

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 177:

#### Question 21:

Which of the following points does not lie in any quadrant?

(a) (3, –6)

(b) (–3, 4)

(c) (5, 7)

(d) (0, 3)

#### Answer:

The point (3, –6) lies in the fourth quadrant.

The point (–3, 4) lies in the second quadrant.

The point (5, 7) lies in the first quadrant.

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

Thus, the point (0, 3) does not lie in any quadrant.

Hence, the correct answer is option (d).

#### Page No 177:

#### Question 22:

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:

The points A(0, 6), O(0, 0) and B(6, 0) can be plotted on the Cartesian plane as follows:

Here, ∆AOB is a right triangle right angled at O.

OA = 6 units and OB = 6 units

∴ Area of ∆AOB = $\frac{1}{2}\times \mathrm{OA}\times \mathrm{OB}=\frac{1}{2}\times 6\times 6$ = 18 square units

Hence, the correct answer is option (c).

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