CBSE Class 10 Coordinate geometry Sure Shot Questions Set 10

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

Question. The distance between the point P(1, 4) and Q(4, 0) is
(a) 4
(b) 5
(c) 6
(d) \( 3\sqrt{3} \)
Answer: (b) 5

Question. The points (-5, 1), (1, p) and (4, -2) are collinear if the value of p is
(a) 3
(b) 2
(c) 1
(d) -1
Answer: (d) -1

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
Answer: (a) 3 : 4

Question. If \( (a/3, 4) \) 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
Answer: (c) -12

Question. If the distance between the points (x, -1) and (3, 2) is 5, then the value of x is
(a) -7 or -1
(b) -7 or 1
(c) 7 or 1
(d) 7 or -1
Answer: (d) 7 or -1

Question. If the points P(1, 2), B(0, 0) and C(a, b) are collinear, then
(a) \( 2a = b \)
(b) \( a = -b \)
(c) \( a = 2b \)
(d) \( a = b \)
Answer: (a) \( 2a = b \)

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 the options
Answer: (b) collinear

Question. If the points A(4,3) and B (x,5) are on the circle with centre O(2,3), then the value of x is :
(a) 5
(b) 6
(c) 2
(d) 0
Answer: (c) 2

Question. Which of the points A(1,3), B(-3,2), C(3,4) and D(4,1) is nearest to the origin:
(a) A
(b) B
(c) C
(d) D
Answer: (a) A

Question. If the point (x,y) is equidistant from the point(2,1) and(1,-2), then:
(a) \( x+3y=0 \)
(b) \( 3x+y=0 \)
(c) \( x+2y=0 \)
(d) \( 3x+2y=0 \)
Answer: (a) \( x+3y=0 \)

Question. If points A(5,p), B(1,5), C(2,1) and D(6,2) form a square ABCD , then p=
(a) 7
(b) 3
(c) 6
(d) 8
Answer: (c) 6

Question. The perimeter of the Triangle formed by the points (0,0), (2,0) and (0,2) is:
(a) \( 1- 2\sqrt{2} \)
(b) \( 2\sqrt{2} + 1 \)
(c) \( 4+ \sqrt{2} \)
(d) \( 4 + 2\sqrt{2} \)
Answer: (d) \( 4 + 2\sqrt{2} \)

Question. The x – Coordinate of a point P is twice its Y- Coordinate. If P is equidistant from Q (2,-5) and R(-3,6), Then the Coordinates of P are:
(a) (16,8)
(b) (14,7)
(c) (18,9)
(d) (10,5)
Answer: (a) (16,8)

Question. The distance between the points \( P(a \sin \phi, 0) \) and \( Q (0, -a \cos \phi) \) is:
(a) \( a^2 \)
(b) 1
(c) 2a
(d) a
Answer: (d) a

Question. The Coordinates of the image of the point (-4,5) in Y-axis is:
(a) (4,5)
(b) (4, -5)
(c) (-4,-5)
(d) (0,5)
Answer: (a) (4,5)

Question. If four vertices of a parallelogram taken in order are (-3,-1), (a,b), (3,3) and (4,3), then a:b=
(a) 1:4
(b) 4:1
(c) 1:2
(d) 2:1
Answer: (b) 4:1

Question. If A and B are the points (-3,4) and (2,1) respectively , then the coordinates of the point C on AB produced such that AC=2BC are:
(a) (2,4)
(b) (3,7)
(c) ( 7,-2)
(d) (7,-9)
Answer: (c) ( 7,-2)

Question. P (5,-3) and Q (3,y ) are the points of trisection of the line segment joining A (7,-2) and B(1,-5) , then y equals:
(a) 2
(b) 4
(c) -4
(d) -5/2
Answer: (c) -4

Question. The point which divides the line segment joining the points (7,-6) and (3,4) in ratio 1:2 internally lies in the:
(a) I quadrant
(b) II quadrant
(c) III quadrant
(d) IV quadrant
Answer: (d) IV quadrant

ASSERTION REASONING QUESTIONS

Question. Assertion : The point which divides the line joining the points A(1, 2) and B(- 1, 1) internally in the ratio 1: 2 is \( (-\frac{1}{3}, \frac{5}{3}) \)
Reason: The coordinates of the point P(x, y) which divides the line segment joining the points \( A(x_1, y_1) \) and \( B(x_2, y_2) \) in the ratio \( m_1 : m_2 \) is \( ( \frac{m_1x_2 + m_2x_1}{m_1 + m_2}, \frac{m_1y_2 + m_2y_1}{m_1 + m_2} ) \)
(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.
Answer: (d) Assertion (A) is false but reason (R) is true.

Question. Assertion : The point on the X -axis which if equidistant from the points A(- 2, 3) and B(5, 4) is (2, 0)
Reason: The coordinates of the point P(x, y) which divides the line segment joining the points \( A(x_1, y_1) \) and \( B(x_2, y_2) \) in the ratio \( m_1 : m_2 \) is \( ( \frac{m_1x_2 + m_2x_1}{m_1 + m_2}, \frac{m_1y_2 + m_2y_1}{m_1 + m_2} ) \)
(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.
Answer: (b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).

Question. Assertion : Ratio in which the line \( 3x + 4y = 7 \) divides the line segment joining the points (1, 2) and (- 2, 1) is 3 : 5
Reason : The coordinates of the point P(x, y) which divides the line segment joining the points \( A(x_1, y_1) \) and \( B(x_2, y_2) \) in the ratio \( m_1 : m_2 \) is \( ( \frac{m_1x_2 + m_2x_1}{m_1 + m_2}, \frac{m_1y_2 + m_2y_1}{m_1 + m_2} ) \)
(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.
Answer: (d) Assertion (A) is false but reason (R) is true.

Question. Assertion : 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 -6 and 1.
Reason : The mid-point of the line segment joining the points \( P(x_1, y_1) \) and \( Q(x_2, y_2) \) is \( ( \frac{x_1+x_2}{2}, \frac{y_1+y_2}{2} ) \)
(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.
Answer: (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).

Question. Assertion : The point (0, 4) lies on y -axis.
Reason : The x co-ordinate on the point on y -axis is zero
(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.
Answer: (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).

Question. Assertion : The value of y is 6, for which the distance between the points P(2,- 3) and Q(10, y) is 10.
Reason : Distance between two given points \( A(x_1, y_1) \) and \( B(x_2, y_2) \) is given by, \( \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \)
(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.
Answer: (d) Assertion (A) is false but reason (R) is true.

Question. Assertion : The point (-1, 6) divides the line segment joining the points (-3, 10) and (6, -8) in the ratio 2 : 7 internally.
Reason : Three points A,B and C are collinear if \( AB + BC = AC \)
(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.
Answer: (b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).

Question. Assertion : The possible values of x for which the distance between the points A(x, - 1) and B(5, 3) is 5 units are 2 and 8.
Reason : Distance between two given points \( A(x_1, y_1) \) and \( B(x_2, y_2) \) is given by, \( AB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \)
(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.
Answer: (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).

Question. Assertion : If the points A(4, 3) and B(x, 5) lies on a circle with the centre O(2,3) then the value of x is 2.
Reason : The mid-point of the line segment joining the points \( P(x_1, y_1) \) and \( Q(x_2, y_2) \) is \( ( \frac{x_1+x_2}{2}, \frac{y_1+y_2}{2} ) \)
(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.
Answer: (b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).

Question. Assertion: The co-ordinates of the point which divides the join of A(-5, 11) and B(4,-7) in the ratio 7 : 2 is (2, -3)
Reason : The coordinates of the point P(x, y) which divides the line segment joining the points \( A(x_1, y_1) \) and \( B(x_2, y_2) \) in the ratio \( m_1 : m_2 \) is \( ( \frac{m_1x_2 + m_2x_1}{m_1 + m_2}, \frac{m_1y_2 + m_2y_1}{m_1 + m_2} ) \)
(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.
Answer: (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).