# MCQs for Mathematics Class 10 with Answers Chapter 7 Coordinate Geometry

Students of class 10 Mathematics should refer to MCQ Questions Class 10 Mathematics Coordinate Geometry with answers provided here which is an important chapter in Class 10 Mathematics NCERT textbook. These MCQ for Class 10 Mathematics with Answers have been prepared based on the latest CBSE and NCERT syllabus and examination guidelines for Class 10 Mathematics. The following MCQs can help you to practice and get better marks in the upcoming class 10 Mathematics examination

## Chapter 7 Coordinate Geometry MCQ with Answers Class 10 Mathematics

MCQ Questions Class 10 Mathematics Coordinate Geometry provided below have been prepared by expert teachers of grade 10. These objective questions with solutions are expected to come in the upcoming Standard 10 examinations. Learn the below provided MCQ questions to get better marks in examinations.

Question. If the centroid of a triangle formed by (7, x), (y, –6) and (9, 10) is at (6, 3), then (x, y) =
(a) (4, 5)
(b) (5, 4)
(c) (–5, –2)
(d) (5, 2)

D

Question. The ratio in which the join of (1, –5) and (–4, 5) is divided by x-axis is :
(a) 1 : 1
(b) 1 : 2
(c) 2 : 3
(d) 3 : 5

A

Question. The horizontal and vertical lines drawn to determine the position of a point in a Cartesian planeare called
(a) Intersecting lines
(b) Transversals
(c) Perpendicular lines
(d) X-axis and Y-axis

D

Question. If the area of the triangle formed by the points (x, 2x), (–2, 6) and (3, 1) is 5 sq. units, then value of x is :
(a) 2/ 3 or 2
(b) 3/5 or 2
(c) 3
(d) 5

A

Question. The mid point of the line segment joining A(2a,4) and B(-2,3b) is M (1,2a + 1). The values of aand b are
(a) 2,3
(b) 1,1
(c) -2,-2
(d) 2,2

D

Question. The area of a rhombus (in sq. units) whose vertices taken in order are (3, 0), (4, 5), (–1, 4) and (–2, –1) is:
(a) 12
(b) 24
(c) 48
(d) none of these

B

Question. If the distance between the points (1, 0) and (4, a) is 5, then value of a is :
(a) ± 4
(b) 4
(c) –4
(d) none of these

A

Question. The points (1,1), (-2, 7) and (3, -3) are
(a) vertices of an equilateral triangle
(b) collinear
(c) vertices of an isosceles triangle
(d) none of these

B

Question. The vertices of a triangle are (3, –5), (–7, 4) and (10, –2). The coordinates of its centroid is :
(a) (–2, 1)
(b) (–2, –1)
(c) (2, –1)
(d) (1, 2)

C

Question. The line 3x + y – 9 = 0 divides the line joining the points (1, 3) and (2, 7) internally in the ratio
(a) 3 : 4
(b) 3 : 2
(c) 2 : 3
(d) 4 : 3

A

Question. The coordinates of the point which divide the join of (–1, 7) and (4, –3) in the ratio 2 : 3 is :
(a) (1, 2)
(b) (1, 3)
(c) (–2, 3)
(d) none of these

B

Question. If (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 is :
(a) x = 3, y = – 6
(b) x = – 6, y = 3
(c) x = 6, y = 3
(d) x = 6, y = –3

C

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)

C

Question. The distance between the points (– 1, – 5) and (– 6, 7) is
(a) 144 units
(b) 13 units
(c) 12 units
(d) 169 units

B

Question. The coordinates of the centre of a circle passing through (1, 2), (3, – 4) and (5, – 6) is:
(a) (11, – 2)
(b) (-2, 11)
(c) (11, 2)
(d) (2, 11)

C

Question. The distance between the point P(1, 4) and Q(4, 0) is
(a) 4
(b) 5
(c) 6
(d) 3√3

B

Question. The points (3, 2), (0, 5), (-3, 2) and (0, -1) are the vertices of a quadrilateral. Which quadrilateralis it?
(a) Rectangle
(b) Square
(c) Parallelogram
(d) Rhombus

B

Question. The ordinate of a point is twice its abscissa. If its distance from the point (4,3) is √10, then thecoordinates of the point are
(a) (1,2) or (3,6)
(b) (1,2) or (3,5)
(c) (2,1) or (3,6)
(d) (2,1) or (6,3)

A

Question. The distance of the point P(6,-6) from the origin is equal to
(a) 3 √4 units
(b) 8 units
(c) 6 √2 units
(d) 3 units

C

Question. Origin divides the join of points (1,1) and (2,2) externally in the ratio
(a) 1:2
(b) 1:-2
(c) -1:-2
(d) -1:2

A

Question. The ratio in which (4,5) divides the line segment joining the points (2,3) and (7,8) is
(a) 2:3
(b) -3:2
(c) 3:2
(d) -2:3

A

Question. The values of x and y, if the distance of the point (x,y) from (-3,0) as well as from (3,0) is 4 are
(a) x = 1, y = 7
(b) x = 2, y = 7
(c) x = 0, y = – √7
(d) x = 0, y = ± √7

D

Question. If A and B are the points (-6, 7) and (-1, -5) respectively, then the distance 2AB is equal to
(a) 26
(b) 169
(c) 13
(d) 238

A

Question. The perimeter of a triangle with vertices (0, 4) (0, 0) and (3, 0) is:
(a) 15
(b) 12
(c) 8
(d) 10

B

Question. If (3,0), (2,a), and (b,6) are the vertices of ABC whose centroid is (2,5), then the values of a and bare
(a) a = 3, b = -9
(b) a = 0, b = 2
(c) a = 1, b = 9
(d) a = 9, b = 1

D

Question. If ( , 4) is the mid-point of the segment joining the points P(-6, 5) and R(-2, 3), then the value of‘a’ is
(a) 12
(b) -6
(c) -12
(d) -4

C

Question. The value of k for which the points (2,3/2) ,(-3, -7/ 2 ) and k,(9/2) are collinear is :
(a) 4
(b) 5
(c) -5 /2
(d) 5/2

B

Question. If (a, 0) , (0, b) and (x, y) are collinear, then
(a) ay + bx = ab
(b) ax + by = 1
(c) ax – by = ab
(d) ay – bx = 1

A

Question. The distance of the point P (2, 3) from the x-axis is
(a) 2
(b) 3
(c) 1
(d) 5

B

Question. The area of the triangle formed by (a, b + c), (b, c + a) and (c, a + b) is :
(a) abc
(b) a + b + c
(c) a2b2c2
(d) 0

D

Question. The distance of the point (– 3, 4) from the origin is
(a) 25 units
(b) 1 unit
(c) 7 units
(d) 5 units

D

Question. The distance between the points (3,4) and (8,-6) is
(a) 2√5 units
(b) 3√5 units
(c) √5 units
(d) 5√5 units

D

Question. A line segment is of length 10 units. If the coordinates of its one end are (2, –3) and the abscissa of the other end is 10, then its ordinate is :
(a) 9, 6
(b) 3, –9
(c) –3, 9
(d) 9, –6

B

Question. The ratio in which the x-axis divides the segment joining A(3,6) and B(12,-3) is
(a) 1:2
(b) -2:1
(c) 2:1
(d) -1:-1

C

Question. The area of the triangle formed by joining the mid-points of the sides of the triangle, whosevertices are (0, -1), (2, 1) and (0, 3) is
(a) 4
(b) 2
(c) 3
(d) 1

D

Question. The distance between the points (a, a) and (−√3a,√3a) is
(a) 3√2a units
(b) 2√2a units
(c) 2√2 units
(d) 2 units

B

Question. The value of k for which the points (k, –1), (2, 1) and (4, 5) are collinear is:
(a) 0
(b) 1
(c) –1
(d) 2

B

Question. The distance between the points (a, b) and (–b, a) is :
(a) 2√ a2+b2
(b) √a2 + b2
(c) √2(a2 + b2 )
(d) none of these

C

Question. The area of the triangle whose vertices are A(1, 2), B(-2, 3) and C(-3, -4) is
(a) 11
(b) 22
(c) 33
(d) 21

A

Question. If 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

D

Question. If the point P(m, 3) lies on the line segment joining the points A − 2/5 ,6  and B(2, 8), the value of m is
(a) 3
(b) 2
(c) –3
(d) –4

D

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

D

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)

B

Question. The points (- 5, 0), (0, 4) and (5, 1) are the vertices of a _______
(a) right triangle
(b) isosceles triangle
(c) equilateral triangle
(d) scalene triangle
(e) None of these

D

Question. The points (4, 5), (6, 7) and (8, 9) are ________
(a) collinear
(b) not collinear
(c) the vertices of a right triangle
(d) vertices of an isosceles triangle
(e) None of these

A

Question. The coordinates of circumcentre of the triangle whose vertices are (3, 6),(4, -4) and (3, -5) are
(a) (-3/2 , 0)
(b) (-3/2 , 1/2)
(c) (1/2 , 3)
(d) (1/3 , 3/2)
(e) None of these

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

C

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

C

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

B

Question. If M and N are the points whose coordinates are (ap2 , 2ap) and (a/p2 , 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

C

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

C

Question. Area of the region formed by the lines 3|x| + 2|y| = 6  is
(a) 8 cm2
(b) 10 cm2
(c) 12 cm2
(d) 14 cm2
(e) None of these

C

Question. The distance between the points (cosθ ,sinθ ,) and (cosθ , – sinθ ,) is _______
(a) √3
(b) √2
(c) 2
(d) 1
(e) None of these

B

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)

A

Question. If the point C(k, 4) divides the line segment joining two points A(2, 6) and B(5, 1) in ratio 2 : 3, the value of k is
(a) 15/ 9
(b) 7/ 8
(c) 16/ 5
(d) 9 /10

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

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)

D

Question. The centre of a circle whose end points of a diameter are (–6, 3) and (6, 4) is
(a) (8, –1)
(b) (4, 7)
(c) (0, 7/ 2)
(d) (4, 7/ 2)

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

B

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)

D

Question. Point P divides the line segment joining the points A(–1, 3) and B(9, 8) such that AP/PB = k /1 . If P lies on the line x – y + 2 = 0, the value of k is
(a) 1/ 3
(b) 2/ 5
(c) 2/ 3
(d) 0

C

Question. If the point C(–1, 2) divides internally the line-segment joining the points A(2, 5) and B(x, y) in the ratio 3 : 4, the value of x2 + y2 is
(a) 21
(b) 29
(c) 31
(d) 35

B

Question. The coordinates of a point which divides the line AB, A (1, 3), B (2, –1) in the ratio 3 : 2 internally are
(a) (5 /7 , 3/ 7)
(b) (8/ 5 , 3/ 5)
(c) (9/ 4 , 7/ 4 )
(d) None of these

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)

A

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)

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)

B

Question. The coordinates of the points, which divide the line segment joining P (2, –3) and Q (–4, –6) into three equal parts are
(a) (0, 4), (–1, 9)
(b) (0, –3), (–1, –7)
(c) (0, –4), (–2, –5)
(d) None of these

C

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

B

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)

D

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

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)

C

Question. Points P and Q trisect the line segment joining the points A(–2, 0) and B(0, 8) such that P is near to A. The coordinates of points P and Q, respectively are
(a) (− 4/ 3 , 8/3 ), (−2/3 , 16/3)
(b) (− 3/ 4 , 5/ 8) , (2/ 3 , 1/ 5)
(c) (− 7/ 3 , 4/ 8) , (3/ 7, 6/ 7)
(d) (2/3 , −16/ 3) , (0, 0 )

A

Question. If the coordinates of points A and B are (–2, –2) and (2, –4) respectively, the coordinates of P such that AP = 3/ 7 AB, where P lies on the line segment AB is
(a) (−2/7 , −20/7)
(b) (2/ 7 , 20/ 7 )
(c) (11/ 9 , 7/ 9 , )
(d) (− 11/ 9 , −7/ 9)

A

Question. The value of a, for which point P ( 3/ a , 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

C

Question. In the following questions, a statement of assertion (A) is followed by a statement 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 (–1, 6) divides the line segment joining the points (–3, 10) and (6, –8) in the ratio 2 : 7 internally.
Reason (R): Given three points, i.e. A, B, C form an equilateral triangle, then AB = BC = AC.
2. Assertion (A): Mid-point of a line segment divides line in the ratio 1 : 1.
Reason (R): The ratio in which the point (–3, k) divides the line segment joining the points (–5, 4) and (–2, 3) is 1 : 2.