JEE (Main) Mathematics - CO-ORDINATE GEOMETRY Multiple Choice Questions (MCQs)

1. If the coordinates of a point are (3, -4), what is its distance from the origin?

A) 3

B) 4

C) 5

D) √25

Answer: C

2. Find the distance between the points (2, 3) and (6, 7).

A) 5

B) 4√2

C) 8

D) √52

Answer: B

3. The coordinates of a triangle are A(0, 0), B(3, 4), and C(6, 0). What is the perimeter of the triangle?

A) 12 + √5

B) 10 + √5

C) 15

D) 13

Answer: D

4. The point dividing the line segment joining (2, 3) and (6, 7) in the ratio 1:2 internally is:

A) (3, 4)

B) (4, 5)

C) (4, 6)

D) (5, 6)

Answer: B

5. A line segment joining A(-3, 5) and B(7, -1) is divided into two equal parts. What are the coordinates of the midpoint?

A) (1, 2)

B) (2, 1)

C) (2, 2)

D) (0, 3)

Answer: A

6. The locus of a point equidistant from the points (3, 0) and (-3, 0) is:

A) x = 3

B) y = 0

C) x = 0

D) y = x

Answer: C

7. Find the equation of the locus of a point P(x, y) such that the sum of its distances from (0, 3) and (0, -3) is 10.

A) x² + y² = 25

B) x² + y² = 16

C) x² + y² = 100

D) x² + y² = 9

Answer: A

8. Find the slope of the line passing through (-1, -1) and (2, 3).

A) 3/2

B) 2

C) 1

D) 4/3

Answer: A

9. A line is parallel to 3x + 4y - 5 = 0. What is the slope of this line?

A) -3/4

B) 3/4

C) 4/3

D) -4/3

Answer: A

10. A line passes through the point (1, -2) and has a slope of 2. What is its equation?

A) y = 2x - 4

B) y = x + 2

C) y = 2x + 4

D) y = -2x + 4

Answer: A

11. A line makes an angle of 45° with the positive x-axis. What is its slope?

A) 1

B) √2

C) -1

D) 0

Answer: A

12. If the slope of a line is -1 and it passes through (2, 3), what is its equation?

A) x + y = 5

B) x - y = 1

C) x + y = -1

D) x - y = 5

Answer: A

13. Find the x-intercept of the line 3x + 4y - 12 = 0.

A) 4

B) 3

C) 12

D) 0

Answer: B

14. The point of intersection of the lines 2x + y = 5 and x - y = 3 is:

A) (2, 3)

B) (3, 2)

C) (1, 2)

D) (3, -1)

Answer: B

15. If two lines have slopes m₁ = 2 and m₂ = -1/2, what is the angle between them?

A) 90°

B) 45°

C) 60°

D) 30°

Answer: A