Please refer to Coordinate Geometry MCQ Questions Class 10 Mathematics below. These MCQ questions for Class 10 Mathematics with answers have been designed as per the latest NCERT, CBSE books, and syllabus issued for the current academic year. These objective questions for Coordinate Geometry will help you to prepare for the exams and get more marks.

**Coordinate Geometry MCQ Questions Class 10 Mathematics**

Please see solved MCQ Questions for Coordinate Geometry in Class 10 Mathematics. All questions and answers have been prepared by expert faculty of standard 10 based on the latest examination guidelines.

**MCQ Questions Class 10 Mathematics Coordinate Geometry**

**Question. The distance between the points (x _{1},y_{1}) and (x^{2},y^{2}) is given by **

(a) √(x

_{2}+x

_{1})

^{2}+(y

_{2}+y

_{1})

^{2}units

(b) √(x

_{2}+x

_{1})

^{2}−(y

_{2}+y

_{1})

^{2}units

(c) √(x

_{2}-x

_{1})

^{2}−(y

_{2}−y

_{1})

^{2}units

(d) √(x

_{2}−x

_{1})

^{2}+(y

_{2}−y

_{1})

^{2}units

**Answer**

D

**Question. If the mid – point of the line segment joining the points (a, b – 2) and ( – 2, 4) is (2, – 3), then the values of ‘a’ and ‘b’ are **

(a) 6, 8

(b) 6, – 8

(c) 4, – 5

(d) – 6, 8

**Answer**

B

**Question. Find the value of ‘k’, if the point (0, 2) is equidistant from the points (3, k) and (k, 5) **

(a) 2

(b) 0

(c) 1

(d) -1

**Answer**

C

**Question. If the points (x, y), (1, 2) and (7, 0) are collinear, then the relation between ‘x’ and ‘y’ is given by **

(a) 3x – y – 7 = 0

(b) 3x + y + 7 = 0

(c) x + 3y – 7 = 0

(d) x – 3y + 7 = 0

**Answer**

C

**Question. If the distance between the points (p, – 5) and (2, 7) is 13 units, then the value of ‘p’ is **

(a) -3, -7

(b) 3, -7

(c) 3, 7

(d) -3, 7

**Answer**

D

**Question. Three given points will be collinear, if the area of the triangle formed by these points is **

(a) 0 sq. units

(b) 1 sq. units

(c) -1 sq. units

(d) 2 sq. units

**Answer**

A

**Question. The area of the triangle with vertices (a, b+c), (b, c+a) and (c, a+b) is **

(a) a + b + c

(b) a^{2}+b^{2}+c^{2}

(c) 0

(d) (a+b+c)^{2}

**Answer**

C

**Question. The points A(4, – 1), B(6, 0), C(7, 2) and D(5, 1) are the vertices of a **

(a) Square

(b) Parallelogram

(c) Rhombus

(d) Rectangle

**Answer**

C

**Question. If the co – ordinates of a point are ( – 5, 11), then its abscissa is **

(a) -5

(b) 11

(c) 5

(d) -11

**Answer**

A

**Question. If one end of a diameter of a circle is (4, 6) and the centre is ( – 4, 7), then the other end is**

(a) ( – 12, 8)

(b) (8, – 12)

(c) (8, 10)

(d) (8, – 6)

**Answer**

A

**Question. The point where the perpendicular bisector of the line segment joining the points A(2, 5) and B(4, 7) cuts is: **

(a) (3, 6)

(b) (0, 0)

(c) (2, 5)

(d) (6, 3)

**Answer**

A

**Question. The point ( – 3, 5) lies in the ___________ quadrant **

(a) IV

(b) II

(c) III

(d) I

**Answer**

B

**Question. The vertices of a quadrilateral are (1, 7), (4, 2), ( – 1, – 1) and ( – 4, 4). The quadrilateral is a **

(a) rectangle

(b) parallelogram

(c) square

(d) Rhombus

**Answer**

C

**Question. The centroid of a triangle whose vertices are (3, -7), ( -8, 6) and (5, 10) is **

(a) (0, 3)

(b) (1, 3)

(c) (3, 3)

(d) (0, 9)

**Answer**

A

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

(a) AP =1/4 AB

(b) AP =1/2 AB

(c) AP =1/3 AB

(d) AP = PB

**Answer**

B

**Question. If the points (x, y), (1, 2) and (7, 0) are collinear, then the relation between ‘x’ and ‘y’ is given by **

(a) 3x – y – 7 = 0

(b) 3x + y + 7 = 0

(c) x + 3y – 7 = 0

(d) x –3y + 7 =0

**Answer**

C

**Question. The distance between the points and is **

(a) 0 units

(b) p units

(c) p^{2} units

(d) 1 units

**Answer**

B

**Question. If the vertices of a triangle are (1, 1), ( – 2, 7) and (3, – 3), then its area is **

(a) 0 sq. units

(b) 2 sq. units

(c) 24 sq. units

(d) 12 sq. units

**Answer**

A

**Question. The triangle whose vertices are ( – 3, 0), (1, – 3) and (4, 1) is ___________ triangle. **

(a) Obtuse triangle

(b) equilateral

(c) right angled isosceles

(d) scalene

**Answer**

C

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

(a) 12 units

(b) 5 units

(c) 13 units

(d) -5 units

**Answer**

B

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

(a) 15 units

(b) 10 units

(c) 9 units

(d) 12 units

**Answer**

D

**Question. AOBC is a rectangle whose three vertices are A(0, 3), O(0, 0) and B(5, 0). The length of its diagonal is **

(a) 2√34 units

(b) 3 units

(c) √34 units

(d) 4 units

**Answer**

C

**Question. A circle has its centre at the origin and a point P(5, 0) lies on it. Then the point Q(8, 6) lies ________ the circle. **

(a) in side

(b) out side

(c) on

(d) None of these

**Answer**

B

**Question. The point where the medians of a triangle meet is called the ________ of the triangle **

(a) circumcentre

(b) centroid

(c) orthocentre

(d) None of these

**Answer**

B

**Question. The points A(1, 2), B(5, 4), C(3, 8) and D( – 1, 6) are the vertices of a **

(a) Rectangle

(b) Rhombus

(c) Square

(d) Parallelogram

**Answer**

C

**Question. The coordinates 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. The centre of a circle is (2a – 1, 7) and it passes through the point (–3, –1). If the diameter of the circle is 20 units, then the value of a is **

(a) α = –2, 3

(b) α = 4, 2

(c) α = 5, –3

(d) α = –4, 2

**Answer**

D

**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 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 A(–2, 5), B(1, –3) and C(a, b) form an isosceles triangle with CB = CA, then 6a – 16b + 19 equals **

(a) 0

(b) 2

(c) 5

(d) 9

**Answer**

A

**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 the distance of P(x, y) from the points A(3, 6) and B(–3, 4) are equal, then 3x + y = **

(a) 4

(b) 5

(c) 8

(d) 12

**Answer**

B

**Question. If two vertices of an equilateral triangle are (3, 0) and (6, 0), the third vertex is **

(a) (5/7 , 2√2/ 7)

(b) (3, 9)

(c) (9 /2 , 3 √3/2)

(d) None of these

**Answer**

C

**Question. If the 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. A relation between x and y such that the point (x, y) is equidistant from the points (7, 1) and (3, 5), is **

(a) x + y = 2

(b) x – y = 2

(c) 2x + y = 8

(d) None of these

**Answer**

B

**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. Point A lies on the line segment PQ joining P(6, –6) and Q(–4, –1) in such a way that PA/ PQ = 2/ 5 . If point P also lies on the line 3x + k(y + 1) = 0, the value of k is **

(a) k = 12/ 5

(b) k = 9 /5

(c) k = 18/5

(d) k = 0

**Answer**

C

**Question. The value of k if the triangle formed by A(8, –10), B(7, –3) and C(0, k) is right-angled at B, is **

(a) k = 2

(b) k = –2

(c) k = 4

(d) k = –4

**Answer**

D

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

(a) 3 1

(b) –3

(c) 4

(d) 5

**Answer**

C

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

(a) 4

(b) 5

(c) 7

(d) 8

**Answer**

B

**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. AOBC is a rectangle whose three vertices are A(0, –3), O(0, 0) and B(4, 0). The length of its diagonal is **

(a) 3 units

(b) 5 units

(c) 7 units

(d) 9 units

**Answer**

B

**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 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 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. Points A(3, 1), B(5, 1), C(a, b) and D(4, 3) are vertices of a parallelogram ABCD. The values of a and b are respectively **

(a) a = 6, b = 3

(b) a = 2, b = 1

(c) a = 4, b = 2

(d) None of these

**Answer**

A

**Question. The x-coordinate of a point P is twice its y-coordinate. If P is equidistant from Q(2, –5) and R(–3, 6), the coordinates of P are **

(a) (12, 6)

(b) (8, 9)

(c) (4, 11)

(d) (16, 8)

**Answer**

D

**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. 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. 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 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. 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 distance between the points (2, 3) and (4, 1) is **

(a) √2

(b) 2 √2

(c) √3

(d) 3 √3

**Answer**

B

**Question. The distance between the points (–5, 7) and (–1, 3) is **

(a) 4 √3

(b) 4 √5

(c) 4 √2

(d) 4 √7

**Answer**

C

**Question. The value of a, so that the point (4, a) lies on the line 3x – 2y = 5 is **

(a) 2

(b) 3

(c) 7/ 2

(d) 5/ 2

**Answer**

C

**Question. (5, –2), (6, 4) and (7, –2) are the vertices of a/an **

(a) Scalene triangle

(b) Equilateral triangle

(c) Isosceles triangle

(d) None of these

**Answer**

C

**Question. The point on the y-axis which is equidistant from (2, –5) and (–2, 9) is **

(a) (0, 3)

(b) (0, 2)

(c) (0, 5)

(d) None of these

**Answer**

B

**Question. The coordinates of the points P and Q are respectively (4, –3) and (–1, 7). The x-coordinate (abscissa) of a point R on the line segment PQ such that PQ/ PR = 5/ 3 , is **

(a) 0

(b) 1

(c) 2

(d) 3

**Answer**

B

**Question. The ratio in which the line 2x + y – 4 = 0 divides the line segment joining the points A (2, –2) and B (3, 7) is **

(a) 3 : 5

(b) 2 : 9

(c) 5 : 7

(d) 4 : 5

**Answer**

B

**Question. Let P and Q be the points of trisection of the line segment joining the points A (2, – 2) and B (–7, 4) such that P is nearer to A. The coordinates of P and Q respectively are **

(a) (3, 2), (1, 9)

(b) (–4, 3), (5, 0)

(c) (–3, 7), (2, 7)

(d) (–1, 0), (–4, 2)

**Answer**

D

**Question. If (1, 2), (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken in order, x and y respectively are **

(a) x = 6, y = 3

(b) x = 3, y = 6

(c) x = –6, y = –3

(d) x = –3, y = –6

**Answer**

A

**Question. The distance between the points (a cos θ + b sin θ , 0) and (0, a sin θ – b cos θ), is **

(a) a^{2} + b^{2}

(b) a^{2} – b^{2}

(c) √a^{2} + b^{2}

(d) √a^{2} − b^{2}

**Answer**

C

**Question. In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Choose the correct choice as: ****(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).(c) Assertion (A) is true but reason (R) is false.(d) Assertion (A) is false but reason (R) is true.1. Assertion (A): The point (0, 4) lies on y-axis.**

Reason (R): The x-coordinate on the point on y-axis is zero.

2. Assertion (A): The value of y is 6, for which the distance between the points P(2, –3) and Q(10, y) is 10.

Reason (R): Distance between two given points A (x

_{1}, y

_{1}) and B (x

_{2}, y

_{2}) is given by AB = √(x

_{2}– x

_{1})

^{2}+ (y

_{2}– y

_{1})

^{2}

**Answer**

**1. (A) , 2. (D)**

**One Word Questions :**

**Question. (0, 2) and (0, –5) are the co-ordinate of two points lying on _________ axis.**

**Answer**

y

**Question. Find the third vertex of a triangle, if two of its vertices are (–3, 1) and (0, –2) the centroid is at origin.**

**Answer**

(3. 1)

**Question. P is the point of x-axis such that its distance from the origin is 3 units. Find the point Q on y-axis such that OP = OQ.**

**Answer**

(0, 3) or (0, –3)

**Question. Find the distance of a point P(x, y) from the origin (0, 0).**

**Answer**

√x^{2} y^{2}

**Question. A(3, 2) and B(–2, 1) are two vertices of a ΔABC whose centroid G has coordinates (5/3 , -1/3) . 35 Maths–X (E)**

**Answer**

(4, –4)

**Question. What are the coordinates of mid-point of line joining the points (6, –2) and (4, 8)?**

**Answer**

(5, 3)

**Question. Find the coordinates of a point on x-axis which is equidistant from (–2, 5) and (2, –3).**

**Answer**

(–2, 0)

**Question. Find the centroid of a triangle whose vertices are (–2, –3), (–1, 0) and (7, –6)**

**Answer**

(4/3 , -3)

**Question. What are the coordinate of centroid of trinangle formed by the points (–7, 6), (8, 5), (2, –2)?**

**Answer**

(1, 3)

**Question. The base BC of an equilateral triangle ABC with side 10cm lies along x=axis such that the mid-point of the base is at the origin. Find the coordinates of point B.**

**Answer**

(–5, 0)

**Question. What is the x – coordinate of the point which divides the line joining (1, 2) and (2, 3) in the ratio 4 : 3?**

**Answer**

11/7

**Question. Find the coordinates of fourth vertex of the rectangle formed by the points (0, 0), (2, 0) and (0, 3).**

**Answer**

(2, 3)

**Question. What is the area of triangle ABC, whose vertices are A(x1, y1), B(x _{2}, y_{2}) and C(x_{3}, y_{3})**

**Answer**

1/2 [x_{1}(y_{2} − y_{3}) + x_{2}(y_{3} − y_{1}) + x_{3} (y_{1} − y_{2})]

**Question. The points (0, –1), (2, 1), (0, 3) and (–2, 1) are the corners of a square. Find the length of its side.**

**Answer**

√8

**Question. Find the value of k if the distance between (k, 5) and (4, 5) is 5.**

**Answer**

9 or (–1)

**Question. Find the coordinates of points dividing the points (3, 5) and (7, 9) in the ratio 2 : 3.**

**Answer**

(23/5 , 33/5)

**Question. Find the value of y if the points A(5, y), B(1, 5), C(2, 1) and D(6, 2) are the vertices of the square.**

**Answer**

6

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

**Answer**

4/7

**Question. Find the coordinates of a point, which is at a distance of 13 units from the origin and lies on x-axis.**

**Answer**

(13, 0) or (–13, 0)

**Question. Find the coordinates of points which divides line joining (–4, 0) and (0, 6) in the ratio 1 : 3.**

**Answer**

(–3, 1.5)

**Question. Find the ratio in which the line segement joining (–2, –3) and (5, 6) is divided by x-axis.**

**Answer**

1 : 2

**Question. What is the area of ΔABC if points A, B and C are collinear?**

**Answer**

zero

**Question. Find the sum of lengths of the diagonals AC and BD of quadrilateral ABCD if A(3, 0), B(5, 3), C(0, 7) and D(–2, 0).**

**Answer**

2 √58

**Question. Find the third vertex of a triangle if two of its vertices are (–1, 4) and (5, 2) and centroid is (0, –3).**

**Answer**

(–4, –15)

**Question. One end of a diameter of a circle is (2, 3) and the centre is (–2, 5). What are the coordinates of the other end of his diameter?**

**Answer**

(–6, 7)