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Coordinate Geometry MCQs — Mathematics (page 3)

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.

51. A carpenter marks the middle of a plank whose ends are at (15, 40) and (95, 40) (cm). The mark is at:

  1. (80, 0)
  2. (55, 40)
  3. (55, 0)
  4. (40, 40)

Answer: B) (55, 40)

Explanation: Midpoint = ( 15 + 952, 40 ) = (55, 40). SLO M-09-B-06 · Application

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52. The points A(0, 0), B(4, 0) and C(0, 3) form a triangle whose longest side has length:

  1. 7
  2. 4
  3. 7
  4. 5

Answer: D) 5

Explanation: BC = 4^2 + 3^2 = 5; it is the hypotenuse of the right triangle at A. SLO M-09-B-01 · Understanding

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53. The midpoint formula for (x1, y1) and (x2, y2) is:

  1. ( x1 + y12, x2 + y22 )
  2. ( x1 + x22, y1 + y22 )
  3. (x1 + x2, y1 + y2)
  4. ( x2 - x12, y2 - y12 )

Answer: B) ( x1 + x22, y1 + y22 )

Explanation: Average the x-coordinates and average the y-coordinates. SLO M-09-B-02 · Knowledge

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54. A wheelchair ramp rises 1 m over a horizontal distance of 12 m. Its gradient is:

  1. 113
  2. 112
  3. 1213
  4. 12

Answer: B) 112

Explanation: Gradient = rise run = 112. SLO M-09-B-07 · Application

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55. A mobile tower at (3, 2) covers everything within 5 km. Is a house at (7, 6) covered? (1 unit = 1 km)

  1. No, it is about 5.66 km away
  2. No, it is 8 km away
  3. Yes, it is 4 km away
  4. Yes, it is exactly 5 km away

Answer: A) No, it is about 5.66 km away

Explanation: 4^2 + 4^2 = 32 approx 5.66 5. SLO M-09-B-06 · Application

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56. Latitude values range from:

  1. 0^circ to 90^circ only
  2. 0^circ to 360^circ
  3. 90^circ S to 90^circ N
  4. 180^circ W to 180^circ E

Answer: C) 90^circ S to 90^circ N

Explanation: The poles are at 90^circN and 90^circS. SLO M-09-B-07 · Application

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57. Write 3x + 4y - 10 = 0 in normal form.

  1. 35x + 45y = 2
  2. 3x + 4y = 10
  3. 35x + 45y = 10
  4. 34x + y = 52

Answer: A) 35x + 45y = 2

Explanation: Divide by 3^2 + 4^2 = 5: 35x + 45y = 2, so p = 2. SLO M-09-B-09 · Understanding

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58. On a map grid where 1 unit = 5 km, Rawalpindi is at (2, 3) and Murree is at (11, 15). The straight-line distance between them is:

  1. 105 km
  2. 15 km
  3. 150 km
  4. 75 km

Answer: D) 75 km

Explanation: Grid distance = 9^2 + 12^2 = 15 units = 15 5 = 75 km. SLO M-09-B-06 · Application

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59. M(5, -2) is the midpoint of AB and A = (-1, 6). Find B.

  1. (6, -8)
  2. (9, 2)
  3. (11, -10)
  4. (2, 2)

Answer: C) (11, -10)

Explanation: x2 = 2(5) - (-1) = 11 and y2 = 2(-2) - (6) = -10, so B = (11, -10). SLO M-09-B-02 · Knowledge

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60. Find the distance between A(-2, 5) and B(-10, -10).

  1. 23
  2. 305
  3. 18
  4. 17

Answer: D) 17

Explanation: AB = (x2 - x1)^2 + (y2 - y1)^2 = 8^2 + 15^2 = 289 = 17. SLO M-09-B-01 · Understanding

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61. A garden path is to run straight from (0, 2) to (6, 5) (metres). The equation of the path is:

  1. y = 2x + 2
  2. y = 12x + 5
  3. y = 12x + 2
  4. y = 36x + 6

Answer: C) y = 12x + 2

Explanation: Slope = 5 - 26 - 0 = 12 and the y-intercept is 2. SLO M-09-B-07 · Application

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62. The lines x - 3y + 2 = 0 and 2x + y + 5 = 0 are:

  1. the same line
  2. neither parallel nor perpendicular
  3. perpendicular
  4. parallel

Answer: B) neither parallel nor perpendicular

Explanation: Slopes: m1 = 13, m2 = -2. They are not equal and m1 m2 = - 23 neq -1. SLO M-09-B-05 · Understanding

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63. A line that goes down from left to right has:

  1. a negative slope
  2. an undefined slope
  3. a positive slope
  4. zero slope

Answer: A) a negative slope

Explanation: As x increases, y decreases, so Delta yDelta x < 0. SLO M-09-B-03 · Knowledge

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64. Every equation of the form ax + by + c = 0 (with a, b not both zero) represents:

  1. a single point
  2. a circle
  3. a parabola
  4. a straight line

Answer: D) a straight line

Explanation: It is of degree one in x and y, so its graph is a straight line. SLO M-09-B-09 · Understanding

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65. In point-slope form, the line with slope 12 through (4, -3) is:

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

Answer: C) y + 3 = 12(x - 4)

Explanation: Point-slope form is y - y1 = m(x - x1). SLO M-09-B-08 · Understanding

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

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

Answer: B) (-1, 2)

Explanation: M = ( x1 + x22, y1 + y22 ) = ( -22, 42 ) = (-1, 2). SLO M-09-B-02 · Knowledge

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67. Convert y - 3 = -2(x + 1) to general form.

  1. x + 2y - 1 = 0
  2. 2x + y - 1 = 0
  3. 2x - y + 1 = 0
  4. 2x + y + 5 = 0

Answer: B) 2x + y - 1 = 0

Explanation: y - 3 = -2x - 2 Rightarrow 2x + y - 1 = 0. SLO M-09-B-09 · Understanding

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68. If the distance between (a, 0) and (0, 8) is 10, then a =

  1. 6 only
  2. pm 8
  3. pm 6
  4. pm 2

Answer: C) pm 6

Explanation: a^2 + 64 = 100 Rightarrow a^2 = 36 Rightarrow a = pm 6. SLO M-09-B-01 · Understanding

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69. The equation of the line with slope 14 and y-intercept -2 is:

  1. y = 14x + 2
  2. y = - 14x - 2
  3. y = 14x - 2
  4. y = -2x + 14

Answer: C) y = 14x - 2

Explanation: Put m = 14 and c = -2 into y = mx + c. SLO M-09-B-04 · Knowledge

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70. If b = 0 in ax + by + c = 0, the line is:

  1. parallel to y = x
  2. horizontal
  3. vertical
  4. through the origin

Answer: C) vertical

Explanation: It becomes x = - ca, a vertical line. SLO M-09-B-09 · Understanding

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71. The prime meridian (0^circ longitude) passes through:

  1. the equator only
  2. the North Pole only
  3. Greenwich, London
  4. Karachi

Answer: C) Greenwich, London

Explanation: Longitude is measured east or west of the meridian through Greenwich. SLO M-09-B-07 · Application

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72. The lines 5x + 2y + 1 = 0 and 10x + 4y + 9 = 0 are:

  1. neither parallel nor perpendicular
  2. perpendicular
  3. parallel
  4. the same line

Answer: C) parallel

Explanation: Slopes: m1 = - 52, m2 = - 52. They are equal, so the lines are parallel. SLO M-09-B-05 · Understanding

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73. For the line y = 23x - 13, the slope and y-intercept are:

  1. m = 23, c = 13
  2. m = - 13, c = 23
  3. m = 23, c = - 13
  4. m = - 23, c = - 13

Answer: C) m = 23, c = - 13

Explanation: Compare with y = mx + c: m = 23 and c = - 13. SLO M-09-B-04 · Knowledge

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74. The midpoint of the segment joining (a, b) and (-a, -b) is:

  1. (2a, 2b)
  2. (0, 0)
  3. (a, b)
  4. (a, -b)

Answer: B) (0, 0)

Explanation: ( a - a2, b - b2 ) = (0, 0). SLO M-09-B-02 · Knowledge

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75. 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

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