9th class Math, Chapter 7: Coordinate Geometry MCQs

1. The equation of a straight line in the slope-intercept form is written as:

1. (A) y = m(x + c)
2. (B) y − y₁ = m(x − x₁)
3. (C) y = c + mx ✓
4. (D) ax + by + c = 0

2. The gradients of two parallel lines are:

1. (A) equal ✓
2. (B) zero
3. (C) negative reciprocals of each other
4. (D) always undefined

3. If the product of the gradients of two lines is −1, then the lines are:

1. (A) parallel
2. (B) perpendicular ✓
3. (C) collinear
4. (D) coincident

4. The distance between the points P(1, 2) and Q(4, 6) is:

1. (A) 5 ✓
2. (B) 6
3. (C) √13
4. (D) 4

5. The midpoint of the line segment with endpoints (−2, 4) and (6, −2) is:

1. (A) (4, 2)
2. (B) (2, 1) ✓
3. (C) (1, 1)
4. (D) (0, 0)

6. The line passing through the points (1, 2) and (4, 5) is:

1. (A) y = x + 1 ✓
2. (B) y = 2x + 3
3. (C) y = 3x − 2
4. (D) y = x + 2

7. The equation of a line in point-slope form is:

1. (A) y = m(x + c)
2. (B) y − y₁ = m(x − x₁) ✓
3. (C) y = c + mx
4. (D) ax + by + c = 0

8. 2x + 3y − 6 = 0 in the slope-intercept form is:

1. (A) y = −(2/3)x + 2 ✓
2. (B) y = (2/3)x − 2
3. (C) y = (2/3)x + 1
4. (D) y = −(2/3)x − 2

9. The equation of a line in symmetric form is:

1. (A) x/a + y/b = 1
2. (B) (x − x₁)/1 + (y − y₁)/m = (z − z₁)/1
3. (C) (x − x₁)/cos α = (y − y₁)/sin α = r ✓
4. (D) y − y₁ = m(x − x₁)

10. The equation of a line in normal form is:

1. (A) y = mx + c
2. (B) x/a + y/b = 1
3. (C) (x − x₁)/cos α = (y − y₁)/sin α
4. (D) x cos α + y sin α = p ✓

11. The point (3, −2) lies in the quadrant:

1. (A) I
2. (B) II
3. (C) III
4. (D) IV ✓

12. The point (−4, 5) lies in the quadrant:

1. (A) I
2. (B) III
3. (C) IV
4. (D) II ✓

13. A point on the x-axis has the form:

1. (A) (a, −a)
2. (B) (a, 0) ✓
3. (C) (0, b)
4. (D) (a, a)

14. In an ordered pair (x, y), x is called the:

1. (A) quadrant
2. (B) abscissa ✓
3. (C) ordinate
4. (D) origin

15. The distance between (x₁, y₁) and (x₂, y₂) is:

1. (A) (x₂ − x₁)² + (y₂ − y₁)²
2. (B) √((x₂ − x₁)² + (y₂ − y₁)²) ✓
3. (C) (x₂ − x₁) + (y₂ − y₁)
4. (D) √((x₂ + x₁)² + (y₂ + y₁)²)

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

1. (A) 12
2. (B) 5 ✓
3. (C) 7
4. (D) 1

17. The midpoint of the segment joining (x₁, y₁) and (x₂, y₂) is:

1. (A) ((x₂ − x₁)/2, (y₂ − y₁)/2)
2. (B) (x₁x₂/2, y₁y₂/2)
3. (C) ((x₁ + x₂)/2, (y₁ + y₂)/2) ✓
4. (D) (x₁ + x₂, y₁ + y₂)

18. The slope of a horizontal line is:

1. (A) 1
2. (B) undefined
3. (C) −1
4. (D) 0 ✓

19. The slope of a vertical line is:

1. (A) −1
2. (B) undefined ✓
3. (C) 0
4. (D) 1

20. The slope m of a line with inclination α is:

1. (A) tan α ✓
2. (B) sin α
3. (C) cos α
4. (D) cot α