# MCQ Questions For Class 10 Coordinate Geometry

Students can refer to the following MCQ Questions for Class 10 Coordinate Geometry with Answers provided below based on the latest curriculum and examination pattern issued by CBSE and NCERT. Our teachers have provided here collection of multiple choice questions for Coordinate Geometry Class 10 covering all topics in your textbook so that students can assess themselves on all important topics and thoroughly prepare for their exams

## Class 10 Coordinate Geometry MCQs Questions with Answers

We have provided below MCQs questions for Class 10 Coordinate Geometry with answers which will help the students to go through the entire syllabus and practice multiple choice questions provided here with solutions. As Coordinate Geometry MCQs in Class 10 pdf download can be really scoring for students, you should go through all problems and MCQ Questions for Class 10 Maths provided below so that you are able to get more marks in your exams.

Question. The three medians of a Δ PQR intersect at a point S. If the medians are PM, QN & RT and the area of
Δ PQR is 90 cm2 , then the area of the quadrilateral MSRN is ________
(a) 45 cm2 (b) 30 cm2
(c) 15 cm2 (d) 60 cm2
(e) None of these

Ans.

B

Question. The points (6, 1), (8, 2), (9, 4) and (7, 3) are the vertices of a
(a) trapezium
(b) rectangle
(c) square
(d) rhombus
(e) None of these

Ans.

D

Question. If the vertices of a triangle have integral coordinates, then the triangle cannot be
(a) an equilateral triangle
(b) a right triangle
(c) an isosceles triangle
(d) All the above
(e) None of these

Ans.

B

Question. The point which lies on the perpendicular bisector of the line segmen joining the points P (- 3, – 5) and Q (3, 5) is
(a) (-3, 4)
(b) (2, -5)
(c) (0, 0)
(d) (-1, 4)
(e) None of these

Ans.

C

Question. The radius of the circle which passes through the origin (0, 6) and (6, 0) is
(a) 12cm
(b) 6 cm
(c) 3√2 cm
(d) 4√2
(e) None of these

Ans.

C

Question. If A (7/3, m/5) is the midpoint of the line segment joining the points B (3, -2) and C (4, 6), then the value of m is _______
(a) 4
(b) 10
(c) -4
(d) -8
(e) None of these

Ans.

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

Ans.

C

Question. The line segment joining the points (3, – 2) and (4, – 6) is divided by the line 2x + 3y – 11 = 0 in the
ratio m: n externally at point (a, b). Which among the following is true for the given information?
(a) m = 11
(b) n = 21
(c) a – b = 89/10
(d) All the above
(e) None of these

Ans.

D

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

Ans.

C

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

Ans.

C

Question. The area of a triangle formed by the line 4x – 3y + 12 = 0 with the coordinate axes is __________
(a) 3 sq unit
(b) 4 sq unit
(c) 5 sq unit
(d) 6 sq unit
(e) None of these

Ans.

A

Question. The orthecentre of the triangle formed by the lines , 5x – 8y = 10, 16x + 10y = 13 and y-axis, is _____

Ans.

A

Question. If the point A (-3, m) divides the line segment joining the points B (-8, -5) and C (1, – 4) in the ratio a : b, then m equals to
(a) -5/3
(b) 40/3
(c) -40/9
(d) 30/7
(e) None of these

Ans.

C

Question. If the points (a, 0), (0, b) and (1, 1) are collinear then which of the following is true :
(a) 1/a + 1/b =2
(b) 1/a – 1/b = 1
(c) 1/a – 1/b = 2
(d) 1/a + 1/b =1

D

Question. If the mid point of the line joining (3, 4) and (k, 7) is (x, y) and 2x + 2y + 1 = 0. Find the value of k.
(a) 10
(b) –15
(c) 15
(d) –10

B

Question. Which of the following is / are correct? Four points will form :
(a) a rectangle, if opposite sides and diagonals are not equal.
(b) a parallelogram, if opposite sides are not equal.
(c) a square, if all the four sides and diagonals are equal.
(d) a right angle triangle, if sum of squares of any two sides is equal to square of third largest side.

A

Question. If P (x , y) is any point on the line joining the points A (a, 0) and B (0, b), then
(a) x/b+ y/a = 1
(b) x/a + y/b= 1
(c) x/a+ y/b = 1
(d) x/b + y/a = 1

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

D

Question. P is a point on the graph of y = 5x + 3. The coordinates of a point Q are (3, –2). If M is the mid point of PQ, then M must lie on the line represented by
(a) y = 5x + 1
(b) y = 5x – 7
(c) y = 5/ 2 x – 7/ 2
(d) y = 5/ 2 x + 1/ 2

B

Question. P, Q, R are three collinear points. The coordinates of Pand R are (3, 4) and (11, 10) respectively and PQ is equal  to 2.5 units. Coordinates of Q are
(a) (5, 11/2)
(b) (11, 5/2)
(c) (5, –11/2)
(d) (–5, 11/2)

A

Question. Ratio in which the line 3x + 4y = 7 divides the line segment joining the points (1, 2) and (–2, 1) is
(a) 3 : 5
(b) 4 : 6
(c) 4 : 9
(d) None of these

C

Question. The point on the X-axis which is equidistant from the points A(–2, 3) and B(5, 4) is
(a) (0, 2)
(b) (2, 0)
(c) (3, 0)
(d) (–2, 0)

B

Question. The point which divides the line joining the points A (1, 2) and B(–1, 1) internally in the ratio 1 : 2 is
(a) (-1/3,5/3)
(b) (1/3,5/3)
(c) (–1, 5)
(d) (1, 5)

B

Question. C is the mid-point of PQ, if P is (4, x), C is (y, –1) and Q is (–2, 4), then x and y respectively are
(a) – 6 and 1
(b) – 6 and 2
(c) 6 and – 1
(d) 6 and – 2

A

Question. The ratio in which the point (2, y) divides the join of (– 4, 3) and (6, 3) and hence the value of y is
(a) 2 : 3, y = 3
(b) 3 : 2, y = 4
(c) 3 : 2, y = 3
(d) 3 : 2, y = 2

C

Question. The centroid of the triangle whose vertices are (3, –7), (–8, 6) and (5, 10) is
(a) (0, 9)
(b) (0, 3)
(c) (1, 3)
(d) (3, 5)

B

Question. If P = (2, 5), Q = (x, –7) and PQ = 13, what is the value of ‘x’?
(a) 5
(b 3
(c) –3
(d) –5

C

Question. The points A (– 4, – 1), B (–2, – 4), C (4, 0) and D (2, 3) are the vertices of a
(a) Parallelogram
(b) Rectangle
(c) Rhombus
(d) Square

B

Question. The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0)is
(a) 5
(b) 12
(c) 11
(d) 7 +√5

B

Question. If the point P (p, q) is equidistant from the points A (a + b, b – a) and B (a – b, a + b), then
(a) ap = by
(b) bp = ay
(c) ap + bq = 0
(d) bp + aq = 0

B

Question. The distances of a point from the x-axis and the y-axis are 5 and 4 respectively. The coordinates of the point can be
(a) (5, 4)
(b) (5, 0)
(c) (0, 4)
(d) (4, 5)

D

Question. A line l passing through the origin makes an angle q with positive direction of x-axis such that sin  = 3 5 . The coordinates of the point, which lies in the fourth quadrant at a unit distance from the origin and on perpendicular to l, are
(a) ( 3 /5, 4/ 5)
(b) (4/ 5 ,3 ,5 )
(c) (3, –4)
(d) (4, –3)

A

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)

A

Question. The centre of the circle passing through the ponts (6, – 6), (3, – 7) and (3, 3) is
(a) (3, 2)
(b) (–3, –2)
(c) (3, – 2)
(d) (–3, 2)

C

Question. In what ratio is the line segment joining the points (3, 5) & (–4, 2) divided by y–axis?
(a) 3 : 2
(b) 3 : 4
(c) 2 : 3
(d) 4 : 3

B

Question. A circle passes through the vertices of a triangle ABC. If the vertices are A(–2, 5), B(–2, –3), C(2, –3), then the centre of the circle is
(a) (0, 0)
(b) (0, 1)
(c) (–2, 1)
(d) (0, –3)

B

Question. The points (a, b), (a1, b1) and (a – a1, b – b1) are collinear if
(a) ab = a1b1
(b) ab1 = a1b
(c) a = b
(d) a1 = b1

B

Question. Which of the following points is 10 units from the origin?
(a) (– 6, 8)
(b) (– 4, 2)
(c) (– 6, 5)
(d) (6, 4)

A

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)

C

Question. The distance between which of the following two points is 2 units?
(a) (–2, –3) and (–2, –4)
(b) (0, 4) and (0, 6)
(c) (7, 2) and (6, 2)
(d) (4, –3) and (2, 3)

B

Question. In what ratio does the point (–2, 3) divide the line-segment joining the points (–3, 5) and (4, –9) ?
(a) 2 : 3
(b) 1 : 6
(c) 6 : 1
(d) 2 : 1

B

Question. Which of the following is / are not correct ?
Three points will form :
(a) an equilateral triangle, if all the three sides are equal.
(b) an isosceles triangle, if any two sides are equal.
(c) a collinear or a line, if sum of two sides is equal to third side.
(d) a rhombus, if all the four sides are equal.

D

Question. If  (a/3 ,4) is the midpoint of the line segment joining A(–6, 5) and B(–2, 3), then what is the value of ‘a’?
(a) –4
(b) –12
(c) 12
(d) –6

B

Fill in the Blanks :

Question. Point on the X-axis which is equidistant from (2, –5) and (–2, 9) is ………….

–7, 0

Question. Distance between (2, 3) and (4, 1) is …………..

2 √2

Question. (1, 2), (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken in order, then the value of x and y are ………..

6, 3

Question. Points (1, 5), (2, 3) and (– 2, – 11) are ………..

Non-collinear

Question. (5, – 2) (6, 4) and (7, – 2) are the vertices of an ………….. triangle.

isosceles

Question. The distance of the point (x1, y1) from the origin is …………

√x12 + y12

Question. Points (3, 2), (–2, –3) and (2, 3) form a …………. triangle.

right angle

Question. Point (– 4, 6) divide the line segment joining the points A(– 6, 10) and B(3, – 8) in the ratio …………..

2 : 7

Question. Relation between x and y if the points (x, y), (1, 2) and (7, 0) are collinear is ………..

x + 3y = 7

Question. If x – y = 2, then point (x, y) is equidistant from (7, 1) and (………) .

(3, 5

True or False :

Question. The distance of a point (2, 3) from Y-axis is y-units.

False

Question. Coordinates of the point which divides the join of (–1, 7) and (4, –3) in the ratio 2 : 3 is (1, 3).

True

Question. Points (1, 7), (4, 2), (–1, –1) and (– 4, 4) are the vertices of a square.

True

Question. The distance of the point (5, 3) from the X-axis is 5 units

False

Question. The distance between P (x1, y1) and Q (x2, y2) is √(x2+x1)2 + (y2+y1)2

False

Question. Ratio in which the line segment joining the points (– 3, 10) and (6, – 8) is divided by (– 1, 6) is 3 : 7.

False

Question. The coordinates of the point P(x, y) which divides the line segment joining the points A(x1, y1) and B(x2, y2) internally in the ratio m1 : m2 are (m1x2-m2x1/m1+m2,m1y2-m2y1/m1+m2)