MCQs / Mathematics / Coordinate Geometry

Coordinate Geometry MCQs — Mathematics

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.

1. On a map grid where 1 unit = 5 km, Hyderabad is at (2, 1) and Karachi is at (14, 17). The straight-line distance between them is:

  1. 20 km
  2. 200 km
  3. 140 km
  4. 100 km

Answer: D) 100 km

Explanation: Grid distance = 12^2 + 16^2 = 20 units = 20 5 = 100 km. SLO M-09-B-06 · Application

Discuss this question

2. The x- and y-intercepts of 4x - 5y + 20 = 0 are:

  1. 4 and -5
  2. 5 and -4
  3. 20 and 20
  4. -5 and 4

Answer: D) -5 and 4

Explanation: Put y = 0: x = -5. Put x = 0: y = 4. SLO M-09-B-09 · Understanding

Discuss this question

3. Two friends live at (-3, -5) and (9, 3) on a town grid. They meet exactly halfway. The meeting point is:

  1. (-1, 3)
  2. (3, -1)
  3. (12, 8)
  4. (6, 4)

Answer: B) (3, -1)

Explanation: Halfway is the midpoint: (3, -1). SLO M-09-B-06 · Application

Discuss this question

4. Write 2x + 3y = -6 in the form y = mx + c.

  1. y = - 23x - 2
  2. y = - 32x - 2
  3. y = 23x + 2
  4. y = 23x - 2

Answer: A) y = - 23x - 2

Explanation: 3y = -2x - 6 Rightarrow y = - 23x - 2. SLO M-09-B-04 · Knowledge

Discuss this question

5. Two shops are at (-3, 4) and (5, 4) on a straight road. A new shop opens exactly between them at:

  1. (1, 0)
  2. (2, 4)
  3. (4, 4)
  4. (1, 4)

Answer: D) (1, 4)

Explanation: Midpoint = ( -3 + 52, 4 ) = (1, 4). SLO M-09-B-06 · Application

Discuss this question

6. Write 6x - 3y = -9 in the form y = mx + c.

  1. y = -2x + 3
  2. y = 2x + 3
  3. y = -2x - 3
  4. y = 12x + 3

Answer: B) y = 2x + 3

Explanation: -3y = -6x - 9 Rightarrow y = 2x + 3. SLO M-09-B-04 · Knowledge

Discuss this question

7. The distance formula is derived by applying which result to the right-angled triangle formed by two points and lines parallel to the axes?

  1. The section formula
  2. The midpoint formula
  3. Pythagoras' theorem
  4. The angle-sum property

Answer: C) Pythagoras' theorem

Explanation: The horizontal and vertical gaps x2 - x1 and y2 - y1 are the legs of a right triangle; the distance is its hypotenuse. SLO M-09-B-01 · Understanding

Discuss this question

8. For the line y = 3x - 2, the slope and y-intercept are:

  1. m = -2, c = 3
  2. m = 3, c = -2
  3. m = 3, c = 2
  4. m = -3, c = -2

Answer: B) m = 3, c = -2

Explanation: Compare with y = mx + c: m = 3 and c = -2. SLO M-09-B-04 · Knowledge

Discuss this question

9. Find the midpoint of the segment joining (2, -6) and (-2, -8).

  1. (0, -7)
  2. (-2, -1)
  3. (-7, 0)
  4. (0, -14)

Answer: A) (0, -7)

Explanation: M = ( x1 + x22, y1 + y22 ) = ( 02, -142 ) = (0, -7). SLO M-09-B-02 · Knowledge

Discuss this question

10. Find the distance between A(0, 4) and B(-7, -20).

  1. 31
  2. 26
  3. 25
  4. 3 71

Answer: C) 25

Explanation: AB = (x2 - x1)^2 + (y2 - y1)^2 = 7^2 + 24^2 = 625 = 25. SLO M-09-B-01 · Understanding

Discuss this question

11. Which line is parallel to 3x - y + 4 = 0?

  1. y = 3x - 10
  2. x - 3y = 1
  3. y = 13x + 4
  4. y = -3x + 4

Answer: A) y = 3x - 10

Explanation: 3x - y + 4 = 0 Rightarrow y = 3x + 4 has slope 3. SLO M-09-B-05 · Understanding

Discuss this question

12. Find the gradient (slope) of the line through (2, -7) and (3, 6).

  1. - 113
  2. 13
  3. 113
  4. -13

Answer: B) 13

Explanation: m = y2 - y1x2 - x1 = 6 - (-7)3 - 2 = 131 = 13. SLO M-09-B-03 · Knowledge

Discuss this question

13. M(-3, 5) is the midpoint of AB and A = (3, -6). Find B.

  1. (-9, 16)
  2. (-6, 11)
  3. (-3, 4)
  4. (0, - 12)

Answer: A) (-9, 16)

Explanation: x2 = 2(-3) - (3) = -9 and y2 = 2(5) - (-6) = 16, so B = (-9, 16). SLO M-09-B-02 · Knowledge

Discuss this question

14. Two friends live at (2, 3) and (10, 9) on a town grid. They meet exactly halfway. The meeting point is:

  1. (7, 6)
  2. (6, 6)
  3. (4, 3)
  4. (8, 6)

Answer: B) (6, 6)

Explanation: Halfway is the midpoint: (6, 6). SLO M-09-B-06 · Application

Discuss this question

15. The equation y - 15 - 1 = x - 24 - 2 is written in:

  1. point-slope form
  2. two-point form
  3. normal form
  4. slope-intercept form

Answer: B) two-point form

Explanation: y - 15 - 1 = x - 24 - 2 is the two-point form. SLO M-09-B-08 · Understanding

Discuss this question

16. Find the distance between (3, 4) and (7, -2).

  1. 2 14
  2. 10
  3. 98
  4. 2 13

Answer: D) 2 13

Explanation: d = 4^2 + 6^2 = 52 = 2 13. SLO M-09-B-01 · Understanding

Discuss this question

17. Find the distance between (0, 1) and (2, -5).

  1. 2 10
  2. 62
  3. 2 11
  4. 8

Answer: A) 2 10

Explanation: d = 2^2 + 6^2 = 40 = 2 10. SLO M-09-B-01 · Understanding

Discuss this question

18. The line y = 2x - 6 crosses the x-axis at:

  1. (0, -6)
  2. (6, 0)
  3. (-3, 0)
  4. (3, 0)

Answer: D) (3, 0)

Explanation: Put y = 0: 2x = 6, x = 3. SLO M-09-B-04 · Knowledge

Discuss this question

19. An aircraft flies 90 nautical miles east and then 120 nautical miles north. How far is it from its starting point?

  1. 210 nautical miles
  2. 150 nautical miles
  3. 30 nautical miles
  4. 200 nautical miles

Answer: B) 150 nautical miles

Explanation: Place the start at (0, 0); the plane ends at (90, 120). Distance = 90^2 + 120^2 = 150 nautical miles. SLO M-09-B-07 · Application

Discuss this question

20. The x- and y-intercepts of 2x + 3y - 12 = 0 are:

  1. 4 and 6
  2. -12 and -12
  3. -6 and -4
  4. 6 and 4

Answer: D) 6 and 4

Explanation: Put y = 0: x = 6. Put x = 0: y = 4. SLO M-09-B-09 · Understanding

Discuss this question

21. The end points of a diameter of a circle are (1, 7) and (5, -1). The centre of the circle is:

  1. (4, -8)
  2. (2, -4)
  3. (6, 6)
  4. (3, 3)

Answer: D) (3, 3)

Explanation: The centre is the midpoint of the diameter: (3, 3). SLO M-09-B-02 · Knowledge

Discuss this question

22. The distance of the point (6, 8) from the origin is:

  1. 14
  2. 2
  3. 12
  4. 10

Answer: D) 10

Explanation: 6^2 + 8^2 = 10. SLO M-09-B-01 · Understanding

Discuss this question

23. An aircraft flies 300 km east and then 400 km north. How far is it from its starting point?

  1. 550 km
  2. 500 km
  3. 100 km
  4. 700 km

Answer: B) 500 km

Explanation: Place the start at (0, 0); the plane ends at (300, 400). Distance = 300^2 + 400^2 = 500 km. SLO M-09-B-07 · Application

Discuss this question

24. Find the gradient (slope) of the line through (5, 1) and (7, 3).

  1. 3
  2. 1
  3. 2
  4. -1

Answer: B) 1

Explanation: m = y2 - y1x2 - x1 = 3 - 17 - 5 = 22 = 1. SLO M-09-B-03 · Knowledge

Discuss this question

25. 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:

  1. 300 km
  2. 180 km
  3. 114 km
  4. 333 km

Answer: D) 333 km

Explanation: 3 111 = 333 km. SLO M-09-B-07 · Application

Discuss this question

Page 1 of 8 Next

Practise Coordinate Geometry MCQs

More Mathematics chapters