26. A drone flies from (1, 2) to (7, 10) (km). How far does it fly?
- 8 km
- 10 km
- 100 km
- 14 km
Answer: B) 10 km
Explanation: 6^2 + 8^2 = 10 km. SLO M-09-B-06 · Application
MCQs / Mathematics / Coordinate Geometry
Coordinate Geometry MCQs — Mathematics (page 2)
195 multiple-choice questions on Coordinate Geometry from Mathematics, each with the correct answer and, where available, a teacher's explanation. Read through them to revise the chapter, then practise the same questions one by one to test yourself.
27. A square plot has corners (0, 0), (20, 0), (20, 20), (0, 20) m. A sprinkler at the centre must reach the corners. Its range must be at least:
- 20 2 m
- 20 m
- 10 m
- 10 2 m (about 14.1 m)
Answer: D) 10 2 m (about 14.1 m)
Explanation: Centre (10, 10) to a corner: 10^2 + 10^2 = 10 2 approx 14.1 m. SLO M-09-B-06 · Application
28. A line is parallel to a line of slope 43. Its slope is:
- 34
- - 43
- 43
- - 34
Answer: C) 43
Explanation: Parallel lines have equal slopes. SLO M-09-B-05 · Understanding
29. Find the midpoint of the segment joining (6, 2) and (-9, 4).
- (-3, 6)
- (- 152, 1)
- (3, - 32)
- (- 32, 3)
Answer: D) (- 32, 3)
Explanation: M = ( x1 + x22, y1 + y22 ) = ( -32, 62 ) = (- 32, 3). SLO M-09-B-02 · Knowledge
30. The latitude of the equator is:
- 45^circ
- 180^circ
- 0^circ
- 90^circ
Answer: C) 0^circ
Explanation: Latitude is measured north or south from the equator, which is 0^circ. SLO M-09-B-07 · Application
31. Convert x2 + y5 = 1 to general form.
- 5x + 2y - 10 = 0
- 5x - 2y - 10 = 0
- 2x + 5y - 10 = 0
- 5x + 2y + 10 = 0
Answer: A) 5x + 2y - 10 = 0
Explanation: Multiply by 10: 5x + 2y = 10. SLO M-09-B-09 · Understanding
32. The line cuts the x-axis at -4 and the y-axis at -7. In intercept form its equation is:
- x-4 + y-7 = 1
- -4x - 7y = 1
- x-7 + y-4 = 1
- x-4 - y-7 = 1
Answer: A) x-4 + y-7 = 1
Explanation: The intercept form is xa + yb = 1, with a the x-intercept and b the y-intercept. SLO M-09-B-08 · Understanding
33. The slope of a horizontal line is:
- 0
- undefined
- 1
- -1
Answer: A) 0
Explanation: Horizontal: y2 - y1 = 0, so m = 0. SLO M-09-B-03 · Knowledge
34. A line is perpendicular to a line of slope 2. Its slope is:
- 2
- - 12
- 12
- -2
Answer: B) - 12
Explanation: Perpendicular slopes multiply to -1: m2 = - 12 = - 12. SLO M-09-B-05 · Understanding
35. Find the gradient (slope) of the line through (5, -5) and (6, -3).
- 2
- - 12
- 12
- -2
Answer: A) 2
Explanation: m = y2 - y1x2 - x1 = -3 - (-5)6 - 5 = 21 = 2. SLO M-09-B-03 · Knowledge
36. Write 4x - 2y = 8 in the form y = mx + c.
- y = -2x - 4
- y = 2x - 4
- y = -2x + 4
- y = 12x - 4
Answer: B) y = 2x - 4
Explanation: -2y = -4x + 8 Rightarrow y = 2x - 4. SLO M-09-B-04 · Knowledge
37. The slope of a vertical line is:
- undefined
- 0
- -1
- 1
Answer: A) undefined
Explanation: Vertical: x2 - x1 = 0, and division by zero is undefined. SLO M-09-B-03 · Knowledge
38. The lines 2x - y + 3 = 0 and 4x - 2y - 7 = 0 are:
- neither parallel nor perpendicular
- parallel
- perpendicular
- the same line
Answer: B) parallel
Explanation: Slopes: m1 = 2, m2 = 2. They are equal, so the lines are parallel. SLO M-09-B-05 · Understanding
39. Find the equation of the line with slope 2 passing through (1, 5).
- y = 2x + 3
- y = 2x + 5
- y = -2x + 3
- y = 2x - 3
Answer: A) y = 2x + 3
Explanation: 5 = 2(1) + c Rightarrow c = 3, so y = 2x + 3. SLO M-09-B-04 · Knowledge
40. Two towns lie on the same meridian, 5^circ of latitude apart. If 1^circ of latitude approx 111 km, the distance between them is about:
- 116 km
- 500 km
- 300 km
- 555 km
Answer: D) 555 km
Explanation: 5 111 = 555 km. SLO M-09-B-07 · Application
41. Longitude values range from:
- 90^circ S to 90^circ N
- 0^circ to 60^circ
- 0^circ to 90^circ
- 180^circ W to 180^circ E
Answer: D) 180^circ W to 180^circ E
Explanation: Longitude goes 180^circ east and 180^circ west of Greenwich. SLO M-09-B-07 · Application
42. Points A(0, 0) and B(6, 0) are two water pumps. A tank must be placed on the line x = 3, at distance 5 from each pump. One possible position is:
- (3, 4)
- (5, 3)
- (3, 3)
- (3, 5)
Answer: A) (3, 4)
Explanation: 3^2 + y^2 = 5 Rightarrow y = pm 4, so (3, 4) (or (3, -4)). SLO M-09-B-06 · Application
43. Using the two-point form, the equation of the line through (1, 2) and (3, 8) is:
- y = 3x + 1
- y = 3x - 1
- y = -3x - 1
- y = 13x - 1
Answer: B) y = 3x - 1
Explanation: y - y1y2 - y1 = x - x1x2 - x1 gives slope 3 and y = 3x - 1. SLO M-09-B-08 · Understanding
44. A line is perpendicular to a line of slope - 34. Its slope is:
- 34
- - 34
- 43
- - 43
Answer: C) 43
Explanation: Perpendicular slopes multiply to -1, so m2 = 43. SLO M-09-B-05 · Understanding
45. For the line x + 4y - 8 = 0, the slope is:
- 14
- - 14
- 4
- -4
Answer: B) - 14
Explanation: m = - ab = - 14 = - 14. SLO M-09-B-09 · Understanding
46. Find the distance between A(3, -5) and B(23, -26).
- 881
- 41
- 29
- 30
Answer: C) 29
Explanation: AB = (x2 - x1)^2 + (y2 - y1)^2 = 20^2 + 21^2 = 841 = 29. SLO M-09-B-01 · Understanding
47. An aircraft flies 60 km east and then 80 km north. How far is it from its starting point?
- 20 km
- 150 km
- 100 km
- 140 km
Answer: C) 100 km
Explanation: Place the start at (0, 0); the plane ends at (60, 80). Distance = 60^2 + 80^2 = 100 km. SLO M-09-B-07 · Application
48. Convert y = 23x - 4 to general form.
- 3x - 2y - 12 = 0
- 2x + 3y - 12 = 0
- 2x - 3y - 12 = 0
- 2x - 3y + 12 = 0
Answer: C) 2x - 3y - 12 = 0
Explanation: Multiply by 3: 3y = 2x - 12, so 2x - 3y - 12 = 0. SLO M-09-B-09 · Understanding
49. A map uses the scale 1 cm : 2 km. Two villages are at (1, 1) and (4, 5) cm on the map. The real distance is:
- 7 km
- 10 km
- 5 km
- 14 km
Answer: B) 10 km
Explanation: Map distance = 3^2 + 4^2 = 5 cm, so real distance = 5 2 = 10 km. SLO M-09-B-07 · Application
50. Two towns lie on the same meridian, 3^circ of latitude apart. If 1^circ of latitude approx 111 km, the distance between them is about:
- 300 km
- 180 km
- 114 km
- 333 km
Answer: D) 333 km
Explanation: 3 111 = 333 km. SLO M-09-B-07 · Application
Practise Coordinate Geometry MCQs