# Coordinate Geometry MCQ Class 10 Mathematics

Please refer to Chapter 7 Coordinate Geometry MCQ Class 10 Mathematics with answers below. These multiple-choice questions have been prepared based on the latest NCERT book for Class 10 Mathematics. Students should refer to MCQ Questions for Class 10 Mathematics with Answers to score more marks in Grade 10 Mathematics exams. Students should read the chapter Coordinate Geometry and then attempt the following objective questions.

**MCQ Questions Class 10 Mathematics Chapter 7 Coordinate Geometry**

The Coordinate Geometry MCQ Class 10 Mathematics provided below covers all important topics given in this chapter. These MCQs will help you to properly prepare for exams.

**Question. If the point C (x, 3) divides the line joining points A(2, 6) and B(5, 2) in the ratio 2 : 1 then the value of x is **

(a) 4

(b) 8

(c) 6

(d) 3

**Answer**

A

**Question. The coordinates of the point where line a x b y + = 7 intersects y-axis are **

(a) (a, 0)

(b) (0, b)

(c) (0, 7b)

(d) (7a, 0)

**Answer**

C

**Question. A point P divides the join of A(5, –2) and B(9, 6) in the ratio 3:1. The co-ordinates of P are **

(a) (4, 7)

(b) (8, 4)

(c) (11/2,5)

(d) (12, 8)

**Answer**

B

**Question. A line intersects the y-axis and x-axis at the points P and Q, respectively. If (2, –5) is the midpoint of PQ, then the coordinates of P and Q are, respectively **

(a) (0, –5) and (2, 0)

(b) (0, 10) and (–4, 0)

(c) (0, 4) and (–10, 0)

(d) (0, –10) and (4, 0)

**Answer**

D

**Question. Komal was asked to plot a point 10 units on the left of the origin and other points 4 units directly above the origin. Which of the following are the two points? **

(a) (10, 0) and (0, 4)

(b) (–10, 0) and (0, 4)

(c) (10, 0) and (0, –4)

(d) (–10, 0) and (4, 0)

**Answer**

B

**Question. If the point P (2, 1) lies on the line segment joining points A (4, 2) and B (8, 4), then **

(a) AP =1/3 =AB

(b) AP = PB

(c) PB=1/3 =AB

(d) AP =1/2 =AB

**Answer**

D

**Question. If the distance between the points (2, –2) and (–1, x) is 5, one of the values of x is **

(a) –2

(b) 2

(c) –1

(d) 1

**Answer**

B

**Question. The points which lie 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. If C(–1, 1) is the mid point of the line segment joining A(–3, b) and B(1, b + 4), then the value of b is **

(a) 1

(b) 3

(c) –1

(d) 2

**Answer**

C

**Question. The point which divides the line segment joining the points (7, –6) and (3, 4) in ratio 1 : 2 internally lies in the **

(a) I quadrant

(b) II quadrant

(c) III quadrant

(d) IV quadrant

**Answer**

D

**Question. The point on the x-axis which is equidistant from (–4, 0) and (10, 0) is **

(a) (7, 0)

(b) (5, 0)

(c) (0, 0)

(d) (3, 0)

**Answer**

D

**Question. The end points of diameter of circle are (2, 4) and (–3, –1). The radius of the circle is **

(a) 5/√2units/2

(b) 5 √2 units

(c) 3√2 units

(d) ±5√2 units/2

**Answer**

A

**Question. The point A (–5, 6) is at a distance of **

(a) √61 units from origin

(b) √11 units from origin

(c) 61 units from origin

(d) 11 units from origin

**Answer**

A

**Question. The distance between the points (m, – n) and (– m, n) is **

(a) √m^{2} +n^{2}

(b) m + n

(c) 2 √m^{2}+n^{2}

(d) √2m^{2} +2n^{2}

**Answer**

C

**Question. The distance of the point P (–6, 8) from the origin is **

(a) 8 units

(b) 2 √7 units

(c) 10 units

(d) 6 units

**Answer**

C

**Question. The perpendicular bisector of the line segment joining the points A (1, 5) and B (4, 6) cuts the y-axis at **

(a) (0, 13)

(b) (0, –13)

(c) (0, 12)

(d) (13, 0)

**Answer**

A

**Question. The distance between the points A (0, 6) and B (0, –2) is **

(a) 6 units

(b) 8 units

(c) 4 units

(d) 2 units

**Answer**

B

**Question. The coordinates of the point which is equidistant from the three vertices of the triangle shown in the given figure are **

(a) (x, y)

(b) (y, x)

(c) (x/2,y/2)

(d) (y/2,x/2)

**Answer**

A

**Question. The distance of the point P (2, 3) from the x-axis is **

(a) 2 units

(b) 3 units

(c) 1 units

(d) 5 units

**Answer**

B

**Question. Point on y-axis has coordinate **

(a) (–a, b)

(b) (a, 0)

(c) (0, b)

(d) (– a, – b)

**Answer**

C

**Question. The points A (9, 0), B (9, 6), C (–9, 6) and D (–9, 0) are the vertices of a **

(a) square

(b) rectangle

(c) rhombus

(d) trapezium

**Answer**

B

**Question. The mid-point of the line segment joining the points A (–2, 8) and B (–6, –4) is **

(a) (–4, –6)

(b) (2, 6)

(c) (–4, 2)

(d) (4, 2)

**Answer**

C

**Question. The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is **

(a) 5 units

(b) 12 units

(c) 11 units

(d) 10 units

**Answer**

B

**Question. The centre of a circle whose end points of a diameter are (–6, 3) and (6, 4) is **

(a) (8, –8)

(b) (4, 7)

(c) (0, 7/2)

(d) (4, 7/2)

**Answer**

C

**Question. Three points lie on a vertical line. Which of the following could be those points? **

(a) (– 8, 3), (– 8, 8), (8, 7)

(b) (–8, 7), (–8, –8), (–8, –100)

(c) (4, 3), (5, 3), (–12, 3)

(d) (0, 4), (4, 0), (0, 0)

**Answer**

B

**Question. The distance between the lines 2x + 4 = 0 and x – 5 = 0, is **

(a) 9 units

(b) 1 unit

(c) 5 units

(d) 7 units

**Answer**

D

**Question. On a graph, two-line segments, AB and CD of equal length are drawn. Which of these could be the coordinates of the points, A, B, C and D? **

(a) A(–3, 4), B(–1, –2) and C(3, 4) D(1, 2)

(b) A(3, 4), B(–1, 2) and C(3, 4), D(1, 2)

(c) A(–3, 4), B(–1, 2) and C(3, 4) D(1, 2)

(d) A(–3, –4), B(–1, 2) and C(3, 4), D(1, 2)

**Answer**

C

**Question. If P (a/3), 4m is the mid-point of the line segment joining the points Q (–6, 5) and R (–2, 3), then the value of a is **

(a) –4

(b) –12

(c) 12

(d) –6

**Answer**

B

**Question. The distance between two points, M and N, on a graph is given as √10 ^{ 2}+√7^{2} . The coordinates of point M are (–4, 3). Given that the point N lies in the first quadrant, which of the following is true about the all possible x coordinates of point N? **

(a) They are multiple of 3.

(b) They are multiple of 4.

(c) They are multiple of 5.

(d) They are multiple of 6.

**Answer**

A

**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. On a coordinate grid, the location of a bank is (–4, 8) and the location of a post office is (2, 0). The scale used is 1 unit = 50 m. What is the shortest possible distance between the bank and the post office? **

(a) 200 m

(b) 300 m

(c) 400 m

(d) 500 m

**Answer**

D

**Question. A point G divides a line segment in the ratio 3:7. The segment starts at the origin and ends at a point K having 20 as its abscissa and 40 as its ordinate. Given that G is closer to the origin than to point K, Which of the following are the coordinates of point G? **

(a) (6, 12)

(b) (12, 6)

(c) (14, 28)

(d) (28, 14)

**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. Two poles are to be installed on an elevated road as shown in the diagram. The diagram also shows the starting and ending points of the road. **

**Which of the following are the coordinates of the poles?**

(a) Q (10, 9) and R (12, 8)

(b) Q (10, 9) and R (12, 10)

(c) Q (10, 8) and R (12, 11)

(d) Q (–10, 9) and R (0, 11)

**Answer**

B

**Question. The graph of a circle with centre O with point R on its circumference is shown.**

**What is the side length of the square that circumscribes the circle? **

(a) √41

(b) 2√41

(c) √17

(d) 3√17

**Answer**

B

**Question. The figure shows a parallelogram with one of its vertices intersecting the y-axis at 3 and another vertex intersecting the x-axis at 2.**

**If (m, n) is the intersection point of the diagonals of the parallelogram, which relation is correct? **

(a) m = n – 0.5

(b) m = n – 1.50

(c) m = 0.5 + n

(d) m = 1.50 + n

**Answer**

C

**Question. The point P(1, 2) divides the line joining of A(–2, 1) and B(7, 4) in the ratio **

(a) 1:2

(b) 2:1

(c) 3:2

(d) 2:3

**Answer**

A

**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. Which of the following are the coordinates of the intersection points of the diagonals of the rectangle ABCD with vertices A(0, 3), B(3, 0), C(1, –2) and D(–2, 1)? **

(a) (1/2,1/2)

(b) (-1/2,-1/2)

(c) (1.5, 1.5)

(d) (2, –1)

**Answer**

A

**Question. The points A(0, 6), B(–5, 3) and C(3, 1) are the vertices of a triangle which is **

(a) isosceles

(b) equilateral

(c) scalene

(d) none of these

**Answer**

A

**Question. If A(m/,5) is the mid-point of the line segment joining the points Q(– 6, 7) and R(–2, 3), then the value of m is **

(a) –12

(b) – 4

(c) 12

(d) – 6

**Answer**

A

**Question. lf the point P(k, 0) divides the line segment joining the points A(2, – 2) and B(– 7, 4) in the ratio 1 : 2, then the value of k is **

(a) 1

(b) 2

(c) – 2

(d) – 1

**Answer**

D

**Question. The ratio in which x-axis divides the line segment joining A(2, –3) and B(5, 6) is **

(a) 3 : 5

(b) 1 : 2

(c) 2 : 1

(d) 2 : 3

**Answer**

B

**Question. The point P on x-axis equidistant from the points A (–1, 0) and B (5, 0) is **

(a) (2, 0)

(b) (0, 2)

(c) (3, 0)

(d) (2, 2)

**Answer**

A

**Question. Let A(4, 2), B(6, 5) and C(1, 4) be the vertices of DABC. The median from A meets BC at D. Then the co-ordinates of the point D are **

(a) 5, 2/ 7

(b) (7/2,9/2)

(c) (5/2,3)

(d) (5/2,7/2)

**Answer**

B

**Question. Centre of circle is at (–1, 3) and one end of a diameter has coordinates (2, 5), the co-ordinates of the other end are **

(a) (–4, 1)

(b) (1, –4)

(c) (4, –1)

(d) (3, 2)

**Answer**

A

**Question. If (a, b) is the mid-point of the line segment joining the points A(10, –6) and B(k, 4) and a – 2b = 18, the value of k is **

(a) 30

(b) 22

(c) 4

(d) 40

**Answer**

B

**Question. Point P(a/ 8,4) is the mid-point of the line segment joining the points A (–5, 2) and B (4, 6). The value of ‘a’ is **

(a) – 4

(b) 4

(c) – 8

(d) – 2

**Answer**

A

**Question. The co-ordinates of the point which is reflection of point (–3, 5) in x-axis are **

(a) (3, 5)

(b) (3, –5)

(c) (–3, –5)

(d) (–3, 5)

**Answer**

C

**Question. If the distance between the points (4, p) and (1, 0) is 5, then the value of p is **

(a) 4 only

(b) ± 4

(c) –4 only

(d) 0

**Answer**

B

**Question. The point which divides the line segment joining the points (8, – 9) and (2, 3) in ratio 1 : 2 internally lies in the **

(a) I quadrant

(b) II quadrant

(c) III quadrant

(d) IV quadrant

**Answer**

D

**Question. What point on x-axis is equidistant from the points A(7, 6) and B(–3, 4)? **

(a) (0, 4)

(b) (–4, 0)

(c) (3, 0)

(d) (0, 3)

**Answer**

C

**Question. If the point P (6, 2) divides the line segment joining A (6, 5) and B (4, y) in the ratio 3 : 1, then the value of y is **

(a) 4

(b) 3

(c) 2

(d) 1

**Answer**

D

**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

**Answer**

D

**Question. If three vertices (in order) of a parallelogram are (p + q, p – q), (2p + q, 2p q) and (p – q, p + q), then its fourth vertex is _________ **

(a) (q, – q)

(b) (2q, – 2q)

(c) ( q, – q)

(d) (p, – p)

(e) None of these

**Answer**

C

**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

**Answer**

A

**Question. If the coordinates of mid-point of the sides of a triangle are (21, 7), (- 5, 8, 5) and (10, 8.5), then which among the following is not a vertex of this triangle? **

(a) ( – 16, 10)

(b) (7, 6)

(c) (36, 7)

(d) (6, 7)

(e) None of these

**Answer**

B

**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

**Answer**

B

**Question. The equation of a line, which passes through (3, 4) and the product of whose intercepts on the coordinate axes is 48, is _________ **

(a) 6x + 9y = 48

(b) 8x + 9y = 48

(c) 4x + 3y = 24

(d) 3x + 4y = 24

(e) None of these

**Answer**

C

**Question. The vertices of a Δ PQR are P (1, 2), Q (- 3, 2) and R (5 – 6). Which among the following is a true statement for this triangle PQR? **

(a) Circumcentre of Δ PQR is (- 1, – 4)

(b) Circumradius of Δ PQR is 740 unit

(c) The point where perpendicular bisectors of PQ and PR intersects, is the circumcentre of the triangle PQR.

(d) All the above

(e) None of these

**Answer**

D

**Question. If the equations of three concurrent lines are , px + 6y – 8 = 0, qx + 5y – 8 = 0 and , rx + 4y – 8 = 0, then the value of p + r is __________ **

(a) q

(b) 2q

(c) 3q

(d) 4q

(e) None of these

**Answer**

B

**Question. The ratio in which the line 2x + 3y – 9 = 0 the points (2, 3) and (4, 7) is _________ **

(a) 3 : 1

(b) – 5 : 4

(c) – 1 : 5

(d) 2 : 5

(e) None of these

**Answer**

C

**Question. Find the orthecentre of the triangle ABC having its vertices as A (- 2, – 3), B (2, 1) and C (5, – 2). **

(a) ( – 3, 5)

(b) ( – 4, 6)

(c) (2, 1)

(d) (0, 0)

(e) None of these

**Answer**

C

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