NCERT Exemplar Class 10 Maths - Chapter 7 Coordinate Geometry

1. The distance of the point P (2, 3) from the x-axis is

(A) 2 (B) 3 (C) 1 (D) 5

Correct Answer: (B)

2. The distance between the points A (0, 6) and B (0, –2) is

(A) 6 (B) 8 (C) 4 (D) 2

Correct Answer: (B)

3. The distance of the point P (–6, 8) from the origin is

(A) 8 (B) \(2\sqrt{7}\) (C) 10 (D) 6

Correct Answer: (C)

4. The distance between the points (0, 5) and (–5, 0) is

(A) 5 (B) \(5\sqrt{2}\) (C) \(2\sqrt{5}\) (D) 10

Correct Answer: (B)

5. AOBC is a rectangle whose three vertices are A (0, 3), O (0, 0) and B (5, 0). The length of its diagonal is

(A) 5 (B) 3 (C) \(\sqrt{34}\) (D) 4

Correct Answer: (C)

6. The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is

(A) 5 (B) 12 (C) 11 (D) \(7 + \sqrt{5}\)

Correct Answer: (B)

7. The area of a triangle with vertices A (3, 0), B (7, 0) and C (8, 4) is

(A) 14 (B) 28 (C) 8 (D) 6

Correct Answer: (C)

8. The points (–4, 0), (4, 0), (0, 3) are the vertices of a

(A) right triangle (B) isosceles triangle (C) equilateral triangle (D) scalene triangle

Correct Answer: (B)

9. 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

Correct Answer: (D)

10. 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)

Correct Answer: (A)

11. The fourth vertex D of a parallelogram ABCD whose three vertices are A (–2, 3), B (6, 7) and C (8, 3) is

(A) (0, 1) (B) (0, –1) (C) (–1, 0) (D) (1, 0)

Correct Answer: (B)

12. If the point P (2, 1) lies on the line segment joining points A (4, 2) and B (8, 4), then

(A) \( AP = \dfrac{1}{3} AB \) (B) \( AP = PB \) (C) \( PB = \dfrac{1}{3} AB \) (D) \( AP = \dfrac{1}{2} AB \)

Correct Answer: (D)

13. If \( P\left(\dfrac{a}{3}, 4\right) \) is the mid-point of the line segment joining the points Q (–6, 5) and R (–2, 3), then the value of \( a \) is

(A) –4 (B) –12 (C) 12 (D) –6

Correct Answer: (B)

14. The perpendicular bisector of the line segment joining the points A (1, 5) and B (4, 6) cuts the y-axis at

(A) (0, 13) (B) (0, –13) (C) (0, 12) (D) (13, 0)

Correct Answer: (A)

15. The coordinates of the point which is equidistant from the three vertices of the \(\triangle AOB\) as shown in the Fig. 7.1 is

(A) \( (x, y) \) (B) \( (y, x) \) (C) \( \left(\dfrac{x}{2}, \dfrac{y}{2}\right) \) (D) \( \left(\dfrac{y}{2}, \dfrac{x}{2}\right) \)

Note: Refer to Fig. 7.1 in the original book.

Correct Answer: (A)

16. A circle drawn with origin as the centre passes through \( \left(\dfrac{13}{2}, 0\right) \). The point which does not lie in the interior of the circle is

(A) \( \left(-\dfrac{3}{4}, 1\right) \) (B) \( \left(2, \dfrac{7}{3}\right) \) (C) \( \left(5, -\dfrac{1}{2}\right) \) (D) \( \left(-6, \dfrac{5}{2}\right) \)

Correct Answer: (D)

17. A line intersects the y-axis and x-axis at the points P and Q, respectively. If (2, –5) is the mid-point of PQ, then the coordinates of P and Q are, respectively

(A) (0, –5) and (2, 0) (B) (0, 10) and (–4, 0) (C) (0, 4) and (–10, 0) (D) (0, –10) and (4, 0)

Correct Answer: (D)

18. The area of a triangle with vertices \( (a, b+c) \), \( (b, c+a) \) and \( (c, a+b) \) is

(A) \( (a+b+c)^{2} \) (B) 0 (C) \( a+b+c \) (D) \( abc \)

Correct Answer: (B)

19. If the distance between the points (4, \( p \)) and (1, 0) is 5, then the value of \( p \) is

(A) 4 only (B) \( \pm 4 \) (C) –4 only (D) 0

Correct Answer: (B)

20. If the points A (1, 2), O (0, 0) and C (\( a \), \( b \)) are collinear, then

(A) \( a = b \) (B) \( a = 2b \) (C) \( 2a = b \) (D) \( a = -b \)

Correct Answer: (C)

NCERT Exemplar Problems – Class 10 Mathematics

Chapter 7: Coordinate Geometry