Grade 10 Math Quiz: Coordinate Geometry Questions | Concept of Maths

Question 1

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

A) A) \( 2 \)

B) B) \( 2\sqrt{2} \)

C) C) \( 4 \)

D) D) \( \sqrt{10} \)

Answer

Correct Answer: 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) D) \( (-8, 4) \)

Answer

Correct Answer: A

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: A

Question 4

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

Question 5

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

A) A) Equilateral Triangle

B) B) Isosceles Triangle

C) C) Right-angled Triangle

D) D) None of the above

Answer

Correct Answer: 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) \( x = 6, y = 3 \)

B) B) \( x = 3, y = 6 \)

C) C) \( x = 5, y = 2 \)

D) D) \( x = 2, y = 5 \)

Answer

Correct Answer: A

Question 7

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

A) A) \( 2 \)

B) B) \( 3 \)

C) C) \( 4 \)

D) D) \( 5 \)

Answer

Correct Answer: 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: 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) \( 1 : 5 \)

B) B) \( 5 : 1 \)

C) C) \( 2 : 3 \)

D) D) \( 3 : 2 \)

Answer

Correct Answer: 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: 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. units

B) B) \( 4 \) sq. units

C) C) \( 6 \) sq. units

D) D) \( 8 \) sq. units

Answer

Correct Answer: 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: 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 I

B) B) Quadrant II

C) C) Quadrant III

D) D) Quadrant IV

Answer

Correct Answer: 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: 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) \( 4 \) only

B) B) \( -4 \) only

C) C) \( \pm 4 \)

D) D) \( 0 \)

Answer

Correct Answer: 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: A

Question 17

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

A) A) \( 5 \)

B) B) \( 12 \)

C) C) \( 11 \)

D) D) \( 7 \)

Answer

Correct Answer: B

Question 18

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

A) A) \( 1 : 2 \)

B) B) \( 2 : 1 \)

C) C) \( 1 : 3 \)

D) D) \( 3 : 1 \)

Answer

Correct Answer: 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) \( a + b = 1 \)

B) B) \( \frac{1}{a} + \frac{1}{b} = 1 \)

C) C) \( a + b = ab \)

D) D) Both B and C are true

Answer

Correct Answer: 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. units

B) B) \( 20 \) sq. units

C) C) \( 24 \) sq. units

D) D) \( 48 \) sq. units

Answer

Correct Answer: C

Accepted Answer

Correct Answer: C

Master Coordinate Geometry: Grade 10 Interactive Quiz | Concept of Maths

Master Coordinate Geometry: Grade 10 Interactive Quiz | Concept of Maths

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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 \( (-2, -1) \)?

Grade 10 Math Quiz: Coordinate Geometry Questions | Concept of Maths

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:

Master Coordinate Geometry: Grade 10 Interactive Quiz | Concept of Maths

Master Coordinate Geometry: Grade 10 Interactive Quiz | Concept of Maths

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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 \( (-2, -1) \)?