CBSE Class 10 Mathematics Coordinate Geometry MCQs Set 02

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: 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
Answer: b

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
Answer: c 

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
Answer: b

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)
Answer: 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)
Answer: a