Please refer to the **MCQ Questions for Class 10 Maths Coordinate Geometry **with Answers. The following Coordinate Geometry Class 10 Maths MCQ Questions have been designed based on the current academic year syllabus and examination guidelines for Class 10. Our faculty has designed MCQ Questions for Class 10 Maths with Answers for all chapters as per your NCERT Class 10 Mathematics book.

## Coordinate Geometry Class 10 MCQ Questions with Answers

Please see below Coordinate Geometry Class 10 Mathematics MCQ Questions, solve the questions and compare your answers with the solutions provided below.

**Question. .PQOR is a rectangle whose vertices are Q (0, 7), O (0, 0) and R (- 5, 0). Find the length of its diagonal.**

(a) √84

(b) 8

(c) 12

(d) √74

(e) None of these

## Ans.

D

**Question.** The line which is perpendicular to 5x + 2y – 3 = 0 is _________

(a) 2x – 5y + 8 = 0

(b) 3x – 5y = 9

(c) 4x – 3y = 7

(d) 5x – 2y = 3

(e) None of these

## Ans.

A

**Question.** If M and N are the points whose coordinates are (ap^{2} 2ap) and (a/p^{2}, 2a/p) respectively and S is the point (a, 0), then 1/SM + 1/SN is equal to _________

(a) a

(b) ap

(c) 1/a

(d) 1/ap

(e) None of these

## Ans.

C

**Question.** The point (p, q) divides the line formed by joining the points (p + q, p + q) and (p – q, q – p) in the**ratio _______**

(a) p : q internally

(b) q : p externally

(c) 2 : 1

(d) 1 : 1

(e) None of these

## Ans.

D

** Question. If the points (p, 0), (0, q) and (1, 1) are collinear, then 1/p + 1/q equals to _______**(a) 1 unit

(b) 2 unit

(c) 3 unit

(d) 4 unit

(e) None of these

## Ans.

A

** Question. The ratio, in which the line 5x + 3y = – 9 divides the segment joining the points (2, 3) and (- 3, 4), is ________**(a) 4 : 3

(b) -4 : 3

(c) -14 : 5

(d) -14 : 3

(e) None of these

## Ans.

C

**Question.** The third vertex of a triangle, if two of its vertices are (- 5, 2) and (1, – 3) and the centroid is at (- 2,3), is

(a) (- 2, 5)

(b) (- 2, 10)

(c) (0, 5)

(d) (10, – 2)

(e) None of these

## Ans.

B

**Question. A line 6x + 5y = 30 intersects the coordinate axes. Find the length of the smallest side of the triangle so formed by the axis.**

(a) 3 units

(b) 4 units

(c) 5 units

(d) 6 units

(e) None of these

## Ans.

C

**Question.** The equation of a line whose inclination is 60^{o} an of 5 units on x-axis, is

(a) √3x – y = √3

(b) √3x – y 5 =√3

(c) x – √3y = √3

(d) x -√3y = 5√3

(e) None of these

## Ans.

B

**Question.** Which among the following can be the vertices of an equilateral triangle?

(a) (2, 3), (5, 4), (7, 8)

(b) (3, – 6), (5,-9), (6, – 12)

(c) (3,-3), (-3, 3), ( -3√3, -3√3)

(d) All the above

(e) None of these

## Ans.

A

**Question.** The equation of median drawn from the vertex P to the side QR of a Δ PQR, whose vertices are P (2,**3), Q (- 3, – 5) and R (6, 2), is _______.**

(a) 9x – y = 18

(b) 9x – y = 15

(c) 3x – 8y = 18

(d) 3x + 8y = 15

(e) None of these

## Ans.

B

** Question. If the mid-points of sides of a Δ ABC are P (2, 5), Q (- 3, 8) and R (6, 12), then its vertices are _______**_

(a) (13, 10), ( -9, 2), (2, 14)

(b) (12, 9), ( -8, 1), (1, 15)

(c) (11, 9), ( -7, 1), (1, 15)

(d) ( -12, 8), ( -7, 2), (-2, 15)

(e) None of these

## Ans.

C

**Question.** The length of the diagonal of a square, which can be inscribed in a right triangle of sides 5 cm, 12 cm**and 13 cm, is ______**

## Ans.

B

**Question. The centre of a circle is (2a, a – 7). The value of a if the circle passes through the point (11, –9) and has diameter 10 √2 units is **

(a) a = 3 or 6

(b) a = 5 or 3

(c) a = 7 or 4

(d) None of these

**Answer**

B

**Question. The distance between (√2 + 1, 2) and (1, 2 −√2) is **

(a) 2

(b) 3

(c) 11

(d) 17

**Answer**

A

**Question. The value of k for which the point (0, 2) is equidistant from two points (3, k) and (k, 5) is **

(a) 1

(b) 2

(c) 5

(d) 9

**Answer**

A

**Question. If points (a, 0), (0, b) and (1, 1) are collinear, then the value of 1/a+1/b is **

(a) 1

(b) 2

(c) 5

(d) 9

**Answer**

A

**Question. If the distance between the points (4, k) and (1, 0) is 5, then what can be the possible values of k? **

(a) k = 4

(b) k = –4

(c) k = ± 4

(d) None of these

**Answer**

C

**Question. The value(s) of x, if the distance between the points A(0, 0) and B(x, – 4) is 5 units, is **

(a) ± 2

(b) ± 3

(c) ± 4

(d) ± 5

**Answer**

B

**Question. If point A(0, 2) is equidistant from the points B(3, p) and C(p, 5), the value of p is **

(a) √5 units

(b) √8 units

(c) √10 units

(d) None of these

**Answer**

C

**Question. The distance between the points (-8/5,2) and (2/5,2) is **

(a) 0 units

(b) 1 unit

(c) 2 units

(d) 5 units

**Answer**

C

**Question. The distance of a point from the origin is **

(a) x^{2} + y^{2}

(b) x^{2} – y^{2}

(c) √x^{2} + y^{2}

(d) None of these

**Answer**

C

**Question. The distance of the point P (3, –4) from the origin is **

(a) 7 units

(b) 5 units

(c) 4 units

(d) 3 units

**Answer**

B

**Question. The points (a, a), (–a, –a) and (√− 3a, √3a) are the vertices of a/an **

(a) Equilateral triangle

(b) Isosceles triangle

(c) Scalene triangle

(d) None of these

**Answer**

A

**Question. If the distance of P(x, y) from A(5, 1) and B(–1, 5) are equal, then 3x equals **

(a) y

(b) y/2

(c) 2y

(d) 2/ y

**Answer**

C

**Question. The point on x-axis which is equidistant from the points (2, –2) and (–4, 2) is **

(a) (1, 0)

(b) (2, 0)

(c) (0, 2)

(d) (–1, 0)

**Answer**

D

**Question. The mid-point of the line segment joining the points (–5, 7) and (–1, 3) is **

(a) (–3, 7)

(b) (–3, 5)

(c) (–1, 5)

(d) (5, –3)

**Answer**

B

**Question. The point which lies on the perpendicular bisector of the line segment joining the points A(– 2, – 5) and B(2, 5) is **

(a) (0, 0)

(b) (0, 2)

(c) (2, 0)

(d) (– 2, 0)

**Answer**

A

**Question. What are the coordinates of D? **

(a) (16, 0)

(b) (0, 0)

(c) (0, 16)

(d) (16, 1)

**Answer**

A

**Question. The distance of the point P (–3, –4) from the x-axis (in units) is **

(a) 3

(b) –3

(c) 4

(d) 5

**Answer**

C

**Question. Points A(2, –1), B(3, 4), C(–2, 3), D(–3, –2) are the vertices of a: **

(a) Rectangle

(b) Square

(c) Rhombus

(d) None of these

**Answer**

C

**Question. The distance between the points (3, –2) and (–3, 2) is **

(a) √52 units

(b) 4 √10 units

(c) 2√10 units

(d) 40 units

**Answer**

A

**Question. The value(s) of y, if the distance between the points (2, y) and (– 4, 3) is 10, is **

(a) 11

(b) –5

(c) Both (a) and (b)

(d) None of these

**Answer**

C

**Question. If (3, –6) is the mid-point of the line segment joining (0, 0) and (x, y), then the point (x, y) is **

(a) (–3, 6)

(b) (6, –6)

(c) (6, –12)

(d) (3/2,-3)

**Answer**

C

**Question. If the point C(–1, 2) divides internally the line segment joining A(2, 5) and B in ratio 3 : 4, the coordinates of B are **

(a) B(5, 2)

(b) B(–5, –2)

(c) B(–7, 2)

(d) B(7, –2)

**Answer**

B

**Question. The ratio in which the line segment joining the points (6, 4) and (1, –7) is divided by x-axis is **

(a) 4 : 7

(b) 4 : 5

(c) 4 : 9

(d) 4 : 11

**Answer**

A

**Question. The value of a, for which point P= ( a/3 , 2) is the mid-point of the line segment joining the points Q(–5, 4) and R(–1, 0) is **

(a) –5

(b) –7

(c) –9

(d) –11

**Answer**

C

**Question. The ratio in which the y-axis divides the line segment joining the points (5, –6) and (–1, –4) is **

(a) 1 : 5

(b) 5 : 1

(c) 1 : 7

(d) 7 : 1

**Answer**

B

**Question. The perpendicular distance of A(5, 12) from the y-axis is **

(a) 4

(b) 5

(c) 7

(d) 8

**Answer**

B

**Question. If A(1, 2), B(4, 3) and C(6, 6) are three vertices of parallelogram ABCD, coordinates of D are **

(a) (3, 5)

(b) (2, 7)

(c) (4, 9)

(d) (3, 8)

**Answer**

A

**Question. The value(s) of x for which the distance between the points P(x, 4) and Q(9, 10) is 10 units, is **

(a) 15 or 2

(b) 10 or 9

(c) 17 or 1

(d) None of these

**Answer**

C

**Question. P(–2, 5) and Q(3, 2) are two points. The coordinates of the point R on PQ such that PR = 2QR are **

(a) R (4/3,3)

(b) R (2/3,5)

(c) R (1/3,7)

(d) None of these

**Answer**

D

**Question. The point which divides the line segment joining the points A(0, 5) and B(5, 0) internally in the ratio 2 : 3 is **

(a) (2, 3)

(b) (3, 4)

(c) (–2, 3)

(d) (3, –5)

**Answer**

A

**Question. The coordinates of the point which divides the line segment joining the points (4, –3) and (8, 5) in the ratio 3 : 1 internally are **

(a) P (4, 3)

(b) P (7, 3)

(c) P (3, 5)

(d) P (7, 3)

**Answer**

D

**Question. If the point P(m, 3) lies on the line segment joining the points A (−2/5,6) , 6 and B(2, 8), the value of m is **

(a) 3

(b) 2

(c) –3

(d) –4

**Answer**

D

**Question. Considering A as the origin, what are the coordinates of A? **

(a) (0, 1)

(b) (1, 0)

(c) (0, 0)

(d) (–1, –1)

**Answer**

C

**Question. The coordinates of a point A, where AB is a diameter of the circle with centre (–2, 2) and B is the point with coordinates (3, 4) are **

(a) A(7, 0)

(b) A(5, 0)

(c) A(–5, 0)

(d) A(–7, 0)

**Answer**

D

**Question. What are the coordinates of P? **

(a) (4, 6)

(b) (6, 4)

(c) (4, 5)

(d) (5, 4)

**Answer**

A

**Question. The coordinates of the point P which divides the join of A(–2, 5) and B(3, –5) in the ratio 2 : 3 are **

(a) (1, 0)

(b) (2, 0)

(c) (3, 0)

(d) (0, 1)

**Answer**

D

**Question. What are the coordinates of R? **

(a) (6, 5)

(b) (5, 6)

(c) (6, 0)

(d) (7, 4)

**Answer**

A