CBSE Class 10 Coordinate geometry Sure Shot Questions Set 12

Question. The distance between the points \( A(-1, -5) \) and \( B(-6, 7) \) is
(a) 12 units
(b) 13 units
(c) 14 units
(d) 15 units
Answer: (b) 13 units

Question. If the distance between the points \( A(x, 2) \) and \( B(3, -6) \) is 10 units, then the positive value of \( x \) is
(a) 6
(b) 9
(c) -3
(d) 5
Answer: (b) 9

Question. A triangle with vertices \( A(4, 0), B(-1, -1) \) and \( C(3, 5) \) is/an
(a) equilateral triangle
(b) isosceles triangle
(c) right triangle
(d) right isosceles triangle
Answer: (d) right isosceles triangle

Question. If three points \( A(0, 0), B(3, \sqrt{3}) \) and \( C(3, \lambda) \) form an equilateral triangle, then \( \lambda \) is equal to
(a) 2
(b) -3
(c) -4
(d) \( \pm\sqrt{3} \)
Answer: (d) \( \pm\sqrt{3} \)

Question. Find the points on Y-axis which is equidistant from two points \( A(-3, 4) \) and \( B(3, 6) \) on the same plane.
(a) \( P(0, -5) \)
(b) \( P(0, 5) \)
(c) \( P(0, \pm5) \)
(d) None of the options
Answer: (b) \( P(0, 5) \)

Question. The distance of the point \( P(3, -5) \) from X-axis is
(a) -5 units
(b) 3 units
(c) 5 units
(d) 4 units
Answer: (c) 5 units

Question. The mid-point of \( A(2p, 3) \) and \( B(-4, 6q) \) is (1, 4), then the value of \( p - q \) is
(a) \( \frac{7}{6} \)
(b) \( \frac{13}{6} \)
(c) \( \frac{6}{13} \)
(d) None of the options
Answer: (b) \( \frac{13}{6} \)

Question. Find the ratio, in which the line segment joining points \( A(-3, 10) \) and \( B(6, -8) \) is divided by \( C(-1, 6) \).
(a) 3 : 4
(b) 2 : 7
(c) 7 : 2
(d) None of the options
Answer: (b) 2 : 7

Question. The vertices of a parallelogram in order are \( A(2, 3), B(3, y), C(x, 6) \) and \( D(4, 5) \). Then, \( (x, y) \) is equal to
(a) \( (-5, 4) \)
(b) (4, 5)
(c) (5, 4)
(d) \( (4, -5) \)
Answer: (c) (5, 4)

Question. Find the coordinates of the centroid of a triangle, whose vertices are \( A(0, 6), B(8, 12) \) and \( C(8, 0) \).
(a) \( (\frac{16}{3}, -6) \)
(b) \( (\frac{16}{3}, 6) \)
(c) (16, 2)
(d) None of the options
Answer: (b) \( (\frac{16}{3}, 6) \)

Question. If the centroid of triangle formed by the points \( P(a, b), Q(b, c) \) and \( R(c, a) \) is a origin. Then, the value of \( a + b \) is equal to
(a) 3c
(b) c
(c) -c
(d) \( \frac{c}{3} \)
Answer: (c) -c

Question. The point \( P \) which divides the line segment joining the points \( A(2, -5) \) and \( B(5, 2) \) in the ratio 2 : 3, lies in the quadrant
(a) IV
(b) III
(c) II
(d) I
Answer: (a) IV

Question. If \( A(1, 3) \) and \( B(3, 7) \) are the end points of a diameter of a circle, then the coordinates of centre are
(a) \( (-2, -5) \)
(b) (5, 2)
(c) (2, 4)
(d) (2, 5)
Answer: (d) (2, 5)

Question. Find the ratio, in which the line \( x + 2y - 6 = 0 \) divides the line segment joining the points \( P(1, -3) \) and \( Q(2, 5) \).
(a) 5 : 7
(b) 6 : 11
(c) 11 : 6
(d) 11 : 5
Answer: (c) 11 : 6