Question 1

1. What is the distance between the points (2, 3) and (4, 1)?

A) A) 2B) B) $2\sqrt{2}$C) C) 4D) D) $\sqrt{10}$

Answer

✓ Correct Answer: Option B

Question 2

2. The coordinates of the midpoint of the line segment joining (-2, 8) and (-6, -4) are:

A) A) (-4, 2)B) B) (4, -2)C) C) (-4, -2) D) (-8, 4)

Question 3

3. Find the coordinates of the point which divides the join of (-1, 7) and (4, -3) internally in the ratio 2 : 3.

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

Answer

✓ Correct Answer: Option A

Question 4

4. The distance of the point (-3, 4) from the origin is:

A) A) 3B) B) 4C) C) 5D) D) 7

Answer

✓ Correct Answer: Option C

Question 5

5. The points (3, 2), (-2, -3), and (2, 3) form what kind of triangle?

A) A) Equilateral TriangleB) B) Isosceles TriangleC) C) Right-angled TriangleD) D) None of the above

Answer

✓ Correct Answer: Option C

Question 6

6. If A(1, 2), B(4, y), C(x, 6), and D(3, 5) are the vertices of a parallelogram taken in order, find the values of x and y.

A) A) x = 6, y = 3B) B) x = 3, y = 6C) C) x = 5, y = 2D) D) x = 2, y = 5

Answer

✓ Correct Answer: Option A

Question 7

7. Find the value of k if the points (7, -2), (5, 1), and (3, k) are collinear.

A) A) 2B) B) 3C) C) 4D) D) 5

Answer

✓ Correct Answer: Option C

Question 8

8. A point on the x-axis which is equidistant from (2, -5) and (-2, 9) is:

A) A) (7, 0)B) B) (-7, 0)C) C) (0, 7)D) D) (0, -7)

Answer

✓ Correct Answer: Option B

Question 9

9. The ratio in which the y-axis divides the line segment joining the points (5, -6) and (-1, -4) is:

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

Answer

✓ Correct Answer: Option B

Question 10

10. The coordinates of the centroid of a triangle with vertices (0, 6), (8, 12), and (8, 0) is:

A) A) $\left( \frac{16}{3}, 6 \right)$B) B) $\left( 6, \frac{16}{3} \right)$C) C) (8, 6)D) D) (16, 18)

Answer

✓ Correct Answer: Option A

Question 11

11. The area of the triangle formed by the points A(5, 2), B(4, 7), and C(7, -4) is:

A) A) 2 sq. unitsB) B) 4 sq. unitsC) C) 6 sq. unitsD) D) 8 sq. units

Answer

✓ Correct Answer: Option A

Question 12

12. The distance between the points (a, b) and (-a, -b) is:

A) A) $\sqrt{a^2+b^2}$B) B) $2\sqrt{a^2+b^2}$C) C) $4\sqrt{a^2+b^2}$D) D) a+b

Answer

✓ Correct Answer: Option B

Question 13

13. The point which divides the line segment joining A(2, -5) and B(5, 2) in the ratio 2 : 3 internally lies in the:

A) A) Quadrant IB) B) Quadrant IIC) C) Quadrant IIID) D) Quadrant IV

Answer

✓ Correct Answer: Option D

Question 14

14. If the origin is the midpoint of the line segment joined by the points (2, 3) and (x, y), then the value of (x, y) is:

A) A) (2, -3)B) B) (-2, -3)C) C) (-2, 3)D) D) (3, 2)

Answer

✓ Correct Answer: Option B

Question 15

15. If the distance between the points (4, p) and (1, 0) is 5, then the value(s) of p is:

A) A) 4 onlyB) B) -4 onlyC) C) $\pm 4$D) D) 0

Answer

✓ Correct Answer: Option C

Question 16

16. Find the third vertex of a triangle, if two of its vertices are (-3, 1) and (0, -2) and the centroid is at the origin.

A) A) (3, 1)B) B) (-3, -1)C) C) (1, 3)D) D) (-1, -3)

Answer

✓ Correct Answer: Option A

Question 17

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

A) A) 5B) B) 12C) C) 11D) D) 7

Answer

✓ Correct Answer: Option B

Question 18

18. The ratio in which the x-axis divides the line segment joining (3, 6) and (12, -3) is:

A) A) 1 : 2B) B) 2 : 1C) C) 1 : 3D) D) 3 : 1

Answer

✓ Correct Answer: Option B

Question 19

19. If the points (a, 0), (0, b), and (1, 1) are collinear, then which of the following is true?

A) A) a + b = 1B) B) $\frac{1}{a} + \frac{1}{b} = 1$C) C) a + b = abD) D) Both B and C are true

Answer

✓ Correct Answer: Option D

Question 20

20. What is the area of a rhombus whose vertices, taken in order, are (3, 0), (4, 5), (-1, 4), and (-2, -1)?

A) A) 12 sq. unitsB) B) 20 sq. unitsC) C) 24 sq. unitsD) D) 48 sq. units

Answer

✓ Correct Answer: Option C

Accepted Answer

✓ Correct Answer: Option A

Grade 10 Math Quiz: Coordinate Geometry Questions

1. What is the distance between the points (2, 3) and (4, 1)?

2. The coordinates of the midpoint of the line segment joining (-2, 8) and (-6, -4) are:

3. Find the coordinates of the point which divides the join of (-1, 7) and (4, -3) internally in the ratio 2 : 3.

4. The distance of the point (-3, 4) from the origin is:

5. The points (3, 2), (-2, -3), and (2, 3) form what kind of triangle?

6. If A(1, 2), B(4, y), C(x, 6), and D(3, 5) are the vertices of a parallelogram taken in order, find the values of x and y.

7. Find the value of k if the points (7, -2), (5, 1), and (3, k) are collinear.

8. A point on the x-axis which is equidistant from (2, -5) and (-2, 9) is:

9. The ratio in which the y-axis divides the line segment joining the points (5, -6) and (-1, -4) is:

10. The coordinates of the centroid of a triangle with vertices (0, 6), (8, 12), and (8, 0) is:

11. The area of the triangle formed by the points A(5, 2), B(4, 7), and C(7, -4) is:

12. The distance between the points (a, b) and (-a, -b) is:

13. The point which divides the line segment joining A(2, -5) and B(5, 2) in the ratio 2 : 3 internally lies in the:

14. If the origin is the midpoint of the line segment joined by the points (2, 3) and (x, y), then the value of (x, y) is:

15. If the distance between the points (4, p) and (1, 0) is 5, then the value(s) of p is:

16. Find the third vertex of a triangle, if two of its vertices are (-3, 1) and (0, -2) and the centroid is at the origin.

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

18. The ratio in which the x-axis divides the line segment joining (3, 6) and (12, -3) is:

19. If the points (a, 0), (0, b), and (1, 1) are collinear, then which of the following is true?

20. What is the area of a rhombus whose vertices, taken in order, are (3, 0), (4, 5), (-1, 4), and (-2, -1)?