Math Ncert Exemplar 2019 Solutions for Class 9 Maths Chapter 3 Coordinate Geometry are provided here with simple step-by-step explanations. These solutions for Coordinate Geometry are extremely popular among Class 9 students for Maths Coordinate Geometry Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Math Ncert Exemplar 2019 Book of Class 9 Maths Chapter 3 are provided here for you for free. You will also love the ad-free experience on Meritnation’s Math Ncert Exemplar 2019 Solutions. All Math Ncert Exemplar 2019 Solutions for class Class 9 Maths are prepared by experts and are 100% accurate.

#### Page No 25:

#### Question 1:

Write the correct answer in each of the following :

Point (–3, 5) lies in the

(A) first quadrant

(B) second quadrant

(C) third quadrant

(D) fourth quadrant

#### Answer:

Here, −3 is the abscissa and 5 is the ordinate.

Since, abscissa (*x*-coordinate) is negative and ordinate (*y*-coordinate) is positive. Therefore, the point (–3, 5) will lie in quadrant II.

Hence, the correct answer is option B.

#### Page No 25:

#### Question 2:

Write the correct answer in each of the following :

Signs of the abscissa and ordinate of a point in the second quadrant are respectively

(A) +, +

(B) –, –

(C) –, +

(D) +, –

#### Answer:

In the second quadrant, the abscissa (*x*-coordinate) is negative and ordinate (*y*-coordinate) is positive. Therefore, the correct signs of the ordered pair (*x, y*)* *will be (–, +).

Hence, the correct answer is option C.

#### Page No 25:

#### Question 3:

Write the correct answer in each of the following :

Point (0, –7) lies

(A) on the *x *–axis

(B) in the second quadrant

(C) on the *y*-axis

(D) in the fourth quadrant

#### Answer:

Since abscissa (0) lies on *x-*axis and ordinate ($-$7) lies on negative *y-*axis.

Therefore, the point (0, $-$7) lies on the *y*-axis.

Hence, option C is the correct option.

#### Page No 25:

#### Question 4:

Write the correct answer in each of the following :

Point (–10, 0) lies

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

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

(C) in the third quadrant

(D) in the fourth quadrant

#### Answer:

The abscissa –10 lies on the negative *x-*axis and ordinate is 0, which means it lies on the *y*-axis.

Therefore, the ordered pair $\left(-10,0\right)$ lies on the negative direction of the *x*-axis.

Hence, the correct answer is option A.

#### Page No 25:

#### Question 5:

Write the correct answer in each of the following :

Abscissa of all the points on the *x*-axis is

(A) 0

(B) 1

(C) 2

(D) any number

#### Answer:

All the points on the *x-*axis have ordinate as zero but abscissa can be any value

e.g. $\left(-2,0\right),\left(0,0\right),\left(7,0\right)$ etc.

Therefore, the abscissa of all the points on the *x*-axis is any number.

Hence, the correct answer is option D.

#### Page No 25:

#### Question 6:

Write the correct answer in each of the following :

Ordinate of all points on the *x*-axis is

(A) 0

(B) 1

(C) – 1

(D) any number

#### Answer:

All the points on the *x-*axis have ordinate as zero.

e.g. ($-2,0)$, (0, 0), (8, 0) etc.

Hence, the correct answer is option A.

#### Page No 26:

#### Question 7:

Write the correct answer in each of the following :

The point at which the two coordinate axes meet is called the

(A) abscissa

(B) ordinate

(C) origin

(D) quadrant

#### Answer:

The point at which the two coordinate axes meet is called the origin.

Hence, the correct answer is option C.

#### Page No 26:

#### Question 8:

Write the correct answer in each of the following :

A point both of whose coordinates are negative will lie in

(A) I quadrant

(B) II quadrant

(C) III quadrant

(D) IV quadrant

#### Answer:

A point both of whose coordinates are negative will lie in III quadrant. This is because in the III quadrant, the *x*-coordinate and the *y*-coordinate are negative.

Hence, the correct answer is option C.

#### Page No 26:

#### Question 9:

Write the correct answer in each of the following :

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

(A) lie in II quadrant

(B) lie in III quadrant

(C) lie in IV quadrant

(D) do not lie in the same quadrant

#### Answer:

Points (1, – 1), (2, – 2), (4, – 5) lie in the IV quadrant and (–3, – 4) lie in III quadrant. Thus, they do not lie in the same quadrant.

Hence, the correct answer is option D.

#### Page No 26:

#### Question 10:

Write the correct answer in each of the following :

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

(A) in I quadrant

(B) in II quadrant

(C) on *x *- axis

(D) on *y *- axis

#### Answer:

Given that, the *y*-coordinate is zero.

So, the point is (X, 0) and X can take any value.

Therefore, the point (X, 0) lies on *x*-axis.

Hence, the correct answer is option C.

#### Page No 26:

#### Question 11:

Write the correct answer in each of the following :

The points (–5, 2) and (2, –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:

Locating the two points (–5, 2) and (2, –5) on the cartesian plane,

Therefore, the point (–5, 2) lies in the II quadrant and point (2, –5) lies in the IV quadrant.

Hence, the correct answer is option C.

#### Page No 26:

#### Question 12:

Write the correct answer in each of the following :

If the perpendicular distance of a point P from the *x*-axis is 5 units and the foot of the perpendicular lies on the negative direction of *x*-axis, then the point P has

(A) *x *coordinate = –5

(B) *y *coordinate = 5 only

(C) *y *coordinate = –5 only

(D) *y *coordinate = 5 or –5

#### Answer:

Given that, the length of the perpendicular from the *x-*axis is 5 units.

So, the ordinate of point P will be +5 or –5.

Therefore, the coordinate of point P is (–*x*, 5) or (–*x*, –5).

Hence, the correct answer is option D.

#### Page No 26:

#### Question 13:

Write the correct answer in each of the following :

On plotting the points O(0, 0), A(3, 0), B(3, 4), C(0, 4) and joining OA, AB, BC and CO which of the following figure is obtained?

(A) Square

(B) Rectangle

(C) Trapezium

(D) Rhombus

#### Answer:

Here, the points O(0,0), A(3,0), B(3,4) and C(0,4) when plotted, the following is obtained:

The figure obtained is a rectangle. This is because

AB = OC = 4 units

OA = BC = 3 units

and the opposite sides are parallel to each other.

Hence, the correct answer is option B.

#### Page No 26:

#### Question 14:

Write the correct answer in each of the following :

If P(– 1, 1), Q(3, –4), R(1, –1), S(–2, –3) and T(–4, 4) are plotted on the graph paper, then the point(s) in the fourth quadrant are

(A) P and T

(B) Q and R

(C) Only S

(D) P and R

#### Answer:

A point lying in the fourth quadrant will be of the form (*x*, –*y*).

Therefore, the points Q(3, –4) and R(1, –1) lies in the fourth quadrant.

Hence, the correct answer is option B.

#### Page No 26:

#### Question 15:

Write the correct answer in each of the following :

If the coordinates of the two points are P(–2, 3) and Q(–3, 5), then (abscissa of P) – (abscissa of Q) is

(A) –5

(B) 1

(C) –1

(D) –2

#### Answer:

Given: P(–2, 3) and Q (– 3, 5)

Here, abscissa of P = –2

and abscissa of Q = –3

∴ (abscissa of P) – (abscissa of R) = –2 – (–3)

= –2 + 3

= 1

#### Page No 26:

#### Question 16:

Write the correct answer in each of the following :

If P(5, 1), Q(8, 0), R(0, 4), S(0, 5) and O(0, 0) are plotted on the graph paper, then the point(s) on the *x*-axis are

(A) P and R

(B) R and S

(C) Only Q

(D) Q and O

#### Answer:

A point on* x-*axis will be of the form (*x*, 0) or (–*x*, 0).

Therefore, Q(8, 0) and O(0,0) lie on* x*-axis.

Hence, the correct answer is option D.

#### Page No 26:

#### Question 17:

Write the correct answer in each of the following :

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:

Abscissa is the measurement along the *x*-axis.

Now, signs of coordinate are:

First quadrant ( +, +)

Second quadrant (–, +)

Third quadrant (–, –)

Fourth quadrant (+, –)

So, the abscissa of the point is positive in the first and fourth quadrant.

Hence, the correct answer is option B.

#### Page No 27:

#### Question 18:

Write the correct answer in each of the following :

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

(A) I and II quadrants

(B) II and III quadrants

(C) I and III quadrants

(D) II and IV quadrants

#### Answer:

The signs of the abscissa and ordinate of a point lying in a quadrant are:

First quadrant (+, +)

Second quadrant (+, –)

Third quadrants (–, –)

Fourth quadrant (–, +)

So, the points whose coordinates have different signs lie in II and IV quadrants.

Hence, the correct answer is option D.

#### Page No 27:

#### Question 19:

Write the correct answer in each of the following :

In the given figure, coordinates of P are

(A) (–4, 2)

(B) (–2, 4)

(C) (4, –2)

(D) (2, –4)

#### Answer:

Here, given point P lies in II quadrant. So, its abscissa will be negative and ordinate will be positive.

Also,

Perpendicular distance from *x*-axis is 4.

Therefore, the *y*-coordinate of P is 4.

Again,

Perpendicular distance from *y*-axis is 2.

Therefore, *x*-coordinate of P is –2.

Thus, the coordinate of P is (–2, 4).

Hence, the correct answer is option B.

#### Page No 27:

#### Question 20:

Write the correct answer in each of the following :

In the given figure, the point identified by the coordinates (–5, 3) is

(A) T

(B) R

(C) L

(D) S

#### Answer:

The point (–5, 3) has negative abscissa and positive ordinate. Therefore, it lies in the second quadrant.

The two points on the second quadrant are L(–5, 3) and R(5, –3).

Thus, the point identified by the coordinates (–5, 3) is L.

Hence, the correct answer is option C.

#### Page No 27:

#### Question 21:

Write the correct answer in each of the following :

The point whose ordinate is 4 and which lies on *y*-axis is

(A) (4, 0)

(B) (0, 4)

(C) (1, 4)

(D) (4, 2)

#### Answer:

A point lying on the* y*-axis has coordinate (0, *y*) where *y* can take any value.

Here, *y *= 4.

Therefore, the coordinate of the point will be (0, 4).

Hence, the correct answer is option B.

#### Page No 27:

#### Question 22:

Write the correct answer in each of the following :

Which of the points P(0, 3), Q(1, 0), R(0, –1), S(–5, 0), T(1, 2) do not lie on the *x*-axis?

(A) P and R only

(B) Q and S only

(C) P, R and T

(D) Q, S and T

#### Answer:

Any point which does not lie on the *x*-axis has coordinate of the form (*x*, *y*), where *y* ≠ 0.

Now,

P(0, 3) and *y* = 3 ≠ 0

Q(1, 0) and *y* = 0

R(0, –1) and *y* = –1 ≠ 0

S(–5, 0) and *y* = 0

T(1, 2) and *y* = 2 ≠ 0

Therefore, P, R and T do not lie on *x*-axis.

Hence, the correct answer is option C.

#### Page No 27:

#### Question 23:

Write the correct answer in each of the following :

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

(A) (0, 5)

(B) (5, 0)

(C) (0, –5)

(D) (–5, 0)

#### Answer:

Any point which lies on the *y*-axis has the coordinates (0, *y*), where *y* can take any value.

Here, the point is at a distance of 5 units in the negative direction of *y*-axis.

Therefore, coordinates of point is (0, –5).

Hence, the correct answer is option C.

#### Page No 27:

#### Question 24:

Write the correct answer in each of the following :

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

(A) 3

(B) 4

(C) 5

(D) 7

#### Answer:

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

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

Hence, the correct answer is option A.

#### Page No 28:

#### Question 1:

Write whether the following statements are True or False? Justify your answer.

(i) Point (3, 0) lies in the first quadrant.

(ii) Points (1, –1) and (–1, 1) lie in the same quadrant.

(iii) The coordinates of a point whose ordinate is $-\frac{1}{2}$ and abscissa is 1 are $-\frac{1}{2},1$.

(iv) A point lies on *y*-axis at a distance of 2 units from the *x*-axis. Its coordinates are (2, 0).

(v) (–1, 7) is a point in the II quadrant.

#### Answer:

(i) False.

Since, the ordinate of the point (3, 0) is zero. Therefore, the point lies on *x*-axis.

(ii) False.

In the point (1, –1), the *x*-coordinate is positive and *y*-coordinate is negative. Therefore, it lies in the IV quadrant and in the point (–1, 1), the *x*-coordinate is negative and *y*-coordinate is positive, so it lies is II quadrant.

(iii) False.

A point whose ordinate is $-\frac{1}{2}$ and abscissa is 1 is $\left(1,\frac{-1}{2}\right)$.

(iv) False.

A point that lies on *y*-axis at a distance of 2 units from the *x*-axis is (0, 2).

(v) True.

In the point (–1, 7), the *x*-coordinate is negative and *y*-coordinate is positive. Hence, point will lie in II quadrant.

#### Page No 29:

#### Question 1:

Write the coordinates of each of the points P, Q, R, S, T and O from the Figure.

#### Answer:

Following are the coordinates of the required points:

P → (1, 1)

Q → (–3, 0)

R → (–2, –3)

S → (2, 1)

T → (4, –2)

O → (0, 0)

#### Page No 30:

#### Question 2:

Plot the following points and write the name of the figure obtained by joining them in order:

P(–3, 2), Q(–7, –3), R(6, –3), S(2, 2)

#### Answer:

Given that, the points are P(–3, 2), Q(–7, –3), R(6, –3) and S(2, 2). Plotting the points on graph paper, following figure is obtained:

From the figure,

$\mathrm{PS}\parallel \mathrm{QR}$

Hence, PQRS is a trapezium.

#### Page No 30:

#### Question 3:

Plot the points (*x*, *y*) given by the following table:

x |
2 | 4 | –3 | –2 | 3 | 0 |

y |
4 | 2 | 0 | 5 | –3 | 0 |

#### Answer:

First, name the points as follows:

P(2, 4), Q(4, 2), R(–3, 0), S(–2, 5), T(3, –3), O(0, 0)

Plotting the points on the graph, following is obtained:

#### Page No 30:

#### Question 4:

Plot the following points and check whether they are collinear or not :

(i) (1, 3), (–1, –1), (–2, –3)

(ii) (1, 1), (2, –3), (–1, –2)

(iii) (0, 0), (2, 2), (5, 5)

#### Answer:

(i) (1, 3), (–1, –1), (–2, –3)

Hence, the points (1, 3), (–1, –1) and (–2, –3) are collinear.

(ii) (1, 1) (2, –3) and (–1, –2)

The points (1, 1), (2, –3) and (–1, –2) do not lie in straight line.

Hence, (1, 1), (2, –3) and (–1, –2) are non-collinear.

(iii) (0, 0), (2, 2) and (5, 5)

Hence, the points (0, 0), (2, 2) and (5, 5) are collinear.

#### Page No 30:

#### Question 5:

Without plotting the points, indicate the quadrant in which they will lie, if

(i) ordinate is 5 and abscissa is –3

(ii) abscissa is –5 and ordinate is –3

(iii) abscissa is –5 and ordinate is 3

(iv) ordinate is 5 and abscissa is 3

#### Answer:

(i) Point → (–3, 5)

Here, abscissa is negative and ordinate is positive. So, it lies in II quadrant.

(ii) Point → (–5, –3)

Here abscissa and ordinates both are negative. So, it lies in III quadrant.

(iii) Point → (–5, 3)

Here, abscissa is negative and ordinate is positive. So, it lies in II quadrant.

(iv) Point → (3, 5)

Here, abscissa and ordinate both are positive. So, it lies in I quadrant.

#### Page No 30:

#### Question 6:

In the figure, LM is a line parallel to the *y*-axis at a distance of 3 units.

(i) What are the coordinates of the points P, R and Q?

(ii) What is the difference between the abscissa of the points L and M?

#### Answer:

Given that, LM is a line parallel to *y*-axis at a distance of 3 units.

(i) Coordinates of P = (3, 2)

Coordinate of Q = (3, –1)

Coordinates of R = (3, 0)

(ii) Abscissa of point L = 3, Abscissa of point M = 3

∴ Difference between abscissa of points L and M = 3 – 3

#### Page No 30:

#### Question 7:

In which quadrant or on which axis each of the following points lie?

(–3, 5), (4, –1), (2, 0), (2, 2), (–3, –6)

#### Answer:

Point → (–3, 5)

Here, abscissa is negative and ordinate is positive.

So, the given point lies in quadrant II.

Point → (4, –1)

Here, abscissa is positive and ordinate is negative.

So, the given point lies in quadrant IV.

Point → (2, 0)

Here, abscissa and ordinate both are positive. Also, the ordinate is zero.

So, the given point lies on the *x-*axis.

Point → (2, 2)

Here, abscissa is positive and ordinate both are positive.

So, the given point lies in quadrant I.

Point → (–3, –6)

Here, abscissa and ordinate both are negative.

So, the given point lies in quadrant III.

#### Page No 30:

#### Question 8:

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

A(1, 1), B(1, 0), C(0, 1), D(0, 0), E(0, –1), F(–1, 0), G(0, 5), H(–7, 0), I(3, 3).

#### Answer:

A point lies on* y*-axis if its abscissa or *x*-coordinate is zero.

Hence, C(0, 1), D(0, 0), E(0, –1), G(0, 5) lies on *y*-axis.

#### Page No 30:

#### Question 9:

Plot the points (*x*, *y*) given by the following table.

Use scale 1 cm = 0.25 units

x |
1.25 | 0.25 | 1.5 | –1.75 |

y |
–0.5 | 1 | 1.5 | –0.25 |

#### Answer:

First, name the points as follows:

P(1.25, –0.5), Q(0.25, 1), R(1.5, 1.5), S(–1.75, –0.25)

Plotting the points on the graph, the following is obtained:

#### Page No 31:

#### Question 10:

A point lies on the *x*-axis at a distance of 7 units from the *y*-axis. What are its coordinates? What will be the coordinates if it lies on *y*-axis at a distance of –7 units from *x*-axis?

#### Answer:

Here, the point lies on *x*-axis, so its *y*-coordinate will be zero. Also, the distance from *y*-axis is 7.

Therefore, the point is (7, 0).

Again, the point lies on *y*-axis, so its *x*-coordinate will be zero. Also, the distance from *x*-axis is (–7) units.

Therefore, the point is (0, –7).

#### Page No 31:

#### Question 11:

Find the coordinates of the point

(i) which lies on *x *and *y *axes both.

(ii) whose ordinate is –4 and which lies on *y*-axis.

(iii) whose abscissa is 5 and which lies on *x*-axis.

#### Answer:

(i) The point which lies on *x*-axis* *and *y*-axis both is origin whose coordinates are (0, 0).

(ii) The point whose ordinate is –4 and which lies on *y*-axis is (0, –4)

(iii) The point whose abscissa is 5 and which lies on *x*-axis is (5, 0).

#### Page No 31:

#### Question 12:

Taking 0.5 cm as 1 unit, plot the following points on the graph paper :

A(1, 3), B(–3, –1), C(1, –4), D(–2, 3), E(0, –8), F (1, 0)

#### Answer:

Given Points: A(1, 3), B(–3, –1), C(1, –4), D(–2, 3), E(0, –8), F (1, 0)

#### Page No 32:

#### Question 1:

Points A(5, 3), B(–2, 3) and D(5, –4) are three vertices of a square ABCD. Plot these points on a graph paper and hence find the coordinates of the vertex C.

#### Answer:

Given that, ABCD is a square such that AB, BC, CD and AD are equal.

Plotting the points A(5, 3), B(–2, 3) and D(5, –4) on the graph,

Now, the abscissa of C should be equal to abscissa of B and ordinate of C should be equal to ordinate of D.

Hence, the coordinates of C are (–2, 4).

#### Page No 32:

#### Question 2:

Write the coordinates of the vertices of a rectangle whose length and breadth are 5 and 3 units respectively, one vertex at the origin, the longer side lies on the *x*-axis and one of the vertices lies in the third quadrant.

#### Answer:

Let OABC be the rectangle with coordinate of O(0, 0). Let OA be the longer side.

Since, one of the vertex lies is the third quadrant and length of longer side is 5 units.

Therefore, the coordinates of A is (5, 0).

Now, OC lies on *y*-axis with length 3 units.

Therefore, coordinate of C is (0, –3).

Now, OA ∥ BC.

Thus, ∠ABC = 90° (rectangle)

Therefore, the coordinate of B is (–5, –3).

Hence, the coordinates of rectangle are:

O(0, 0), A(–5, 0), B(–5, –3) and C(0, –3)

#### Page No 32:

#### Question 3:

Plot the points P(1, 0), Q(4, 0) and S(1, 3). Find the coordinates of the point R such that PQRS is a square.

#### Answer:

Given coordinates: P(1, 0), Q(4, 0), S(1, 3)

Since, PQRS is a square.

So, abscissa of R will be equal to abscissa of Q and ordinate of R will be equal to ordinate of S.

Therefore, the coordinate of R is (4, 3).

#### Page No 32:

#### Question 4:

From the given figure, answer the following :

(i) Write the points whose abscissa is 0.

(ii) Write the points whose ordinate is 0.

(iii) Write the points whose abscissa is –5.

#### Answer:

(i) Points whose abscissa zero: A(0, 3), L(0, –4) and O(0, 0)

(ii) Points whose ordinate is zero: G(5, 0), O(0, 0)

(iii) Points whose abscissa is –5: D(–5, 1), H(–5, –3)

#### Page No 32:

#### Question 5:

Plot the points A(1, –1) and B(4, 5)

(i) Draw a line segment joining these points. Write the coordinates of a point on this line segment between the points A and B.

(ii) Extend this line segment and write the coordinates of a point on this line which lies outside the line segment AB.

#### Answer:

First, plot the two points A and B on the graph as follows:

On joining the points A and B, we get the line segment AB.

(i) Now to find the coordinates of a point on this line segment between A and B, draw a perpendicular to *x*-axis from *x *= 3. Let it be point C. Now, draw a perpendicular to *y*-axis from C. It intersects the *y*-axis at *y* = 3. Thus, the point C(3,3) lies between the line segment AB.

(ii) Extend the line segment AB. Now, draw a perpendicular to *x*-axis from *x* = 0.4. Let it intersect the extended line segment at D on *y*-axis at *y* = −2. Thus, we get the point D(0.4,−2) which lies outside the line segment AB.

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