CBSE Class 10 Mathematics Coordinate Geometry MCQs Set 03

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
Answer: b

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 of the options
Answer: b

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
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
Answer: c

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
Answer: c 

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)
Answer: a 

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)
Answer: 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
Answer: d

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
Answer: b 

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: 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.
Answer: 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
Answer: 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
Answer: 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)
Answer: 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
Answer: c

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 the options
Answer: c

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)
Answer: b

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)
Answer: 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
Answer: b

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
Answer: 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
Answer: a 

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)
Answer: c

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
Answer: b

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
Answer: d

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
Answer: b 

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
Answer: 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 of the options
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: 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)
Answer: a

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.
Answer: d

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)
Answer: b

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
Answer: b

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
Answer: 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
Answer: a

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)
Answer: d

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 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)
Answer: c

Fill in the Blanks :

Question: Points (1, 5), (2, 3) and (– 2, – 11) are ...........
Answer: Non-collinear

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 ...........
Answer: 6, 3

Question: Points (3, 2), (–2, –3) and (2, 3) form a ............. triangle.
Answer: right angle

 Question: Point on the X-axis which is equidistant from (2, –5) and (–2, 9) is .............
Answer: –7, 0

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

Question: If x – y = 2, then point (x, y) is equidistant from (7, 1) and (.........) .
Answer: (3, 5)

Question: Distance between (2, 3) and (4, 1) is ..............
Answer: 2 √2

Question: Relation between x and y if the points (x, y), (1, 2) and (7, 0) are collinear is ...........
Answer: x + 3y = 7
Question: The distance of the point (x¹, y¹) from the origin is ............ 
Answer: √x₁² + y₁²

Question: Point (– 4, 6) divide the line segment joining the points A(– 6, 10) and B(3, – 8) in the ratio ..............
Answer: 2 : 7

True or 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)
Answer: False

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

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

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

Question: The ratio in which the point (3, 5) divides the join of (1, 3) and (4, 6) is 2 : 1. 
Answer: True 

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

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

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