MCQs / Mathematics / Coordinate Geometry

Coordinate Geometry MCQs — Mathematics (page 4)

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.

76. Write x + 5y = 10 in the form y = mx + c.

  1. y = -5x + 2
  2. y = - 15x + 2
  3. y = 15x + 2
  4. y = 15x - 2

Answer: B) y = - 15x + 2

Explanation: 5y = -1x + 10 Rightarrow y = - 15x + 2. SLO M-09-B-04 · Knowledge

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77. For the line 5x - 2y - 10 = 0, the slope is:

  1. - 52
  2. 52
  3. - 25
  4. 25

Answer: B) 52

Explanation: m = - ab = - 5-2 = 52. SLO M-09-B-09 · Understanding

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78. A line is parallel to a line of slope - 25. Its slope is:

  1. 25
  2. - 52
  3. - 25
  4. 52

Answer: C) - 25

Explanation: Parallel lines have equal slopes. SLO M-09-B-05 · Understanding

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79. The diagonals of a parallelogram ABCD bisect each other. If A(1, 2), B(5, 3) and C(7, 7), then D is:

  1. (4, 4)
  2. (3, 6)
  3. (11, 8)
  4. (3, 2)

Answer: B) (3, 6)

Explanation: Midpoint of AC = (4, 4.5) must also be the midpoint of BD: D = (2 4 - 5, 2 4.5 - 3) = (3, 6). SLO M-09-B-02 · Knowledge

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80. The normal form of the line whose perpendicular from the origin has length 2 and makes an angle of 30^circ with the x-axis is:

  1. xcos 30^circ + ysin 30^circ = 2
  2. xcos 30^circ + ysin 30^circ = 4
  3. xsin 30^circ + ycos 30^circ = 2
  4. xcos 30^circ - ysin 30^circ = 2

Answer: A) xcos 30^circ + ysin 30^circ = 2

Explanation: Normal form: xcosalpha + ysinalpha = p. Here this is x ( 32 ) + y ( 12 ) = 2. SLO M-09-B-08 · Understanding

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81. For the line 2x + 3y - 12 = 0, the slope is:

  1. 32
  2. 23
  3. - 32
  4. - 23

Answer: D) - 23

Explanation: m = - ab = - 23 = - 23. SLO M-09-B-09 · Understanding

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82. Find the gradient (slope) of the line through (-4, -2) and (-7, 7).

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

Answer: A) -3

Explanation: m = y2 - y1x2 - x1 = 7 - (-2)-7 - (-4) = 9-3 = -3. SLO M-09-B-03 · Knowledge

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83. Two places are 30^circ of longitude apart. Their local times differ by:

  1. 3 hours
  2. 2 hours
  3. 1 hour
  4. 30 minutes

Answer: B) 2 hours

Explanation: 30 div 15 = 2 hours. SLO M-09-B-07 · Application

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84. Write 2x - 5y + 10 = 0 in intercept form.

  1. x-5 + y2 = 1
  2. x-5 - y2 = 1
  3. x2 + y-5 = 1
  4. x5 + y-2 = 1

Answer: A) x-5 + y2 = 1

Explanation: 2x - 5y = -10; divide by -10: x-5 + y2 = 1. SLO M-09-B-09 · Understanding

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85. For the line y = x + 7, the slope and y-intercept are:

  1. m = 1, c = 7
  2. m = -1, c = 7
  3. m = 1, c = -7
  4. m = 7, c = 1

Answer: A) m = 1, c = 7

Explanation: Compare with y = mx + c: m = 1 and c = 7. SLO M-09-B-04 · Knowledge

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86. A football ground has corners at (0, 0) and (100, 60) diagonally opposite (metres). The centre spot is at:

  1. (100, 60)
  2. (60, 100)
  3. (25, 15)
  4. (50, 30)

Answer: D) (50, 30)

Explanation: The centre is the midpoint of the diagonal. SLO M-09-B-06 · Application

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87. In point-slope form, the line with slope - 23 through (3, 4) is:

  1. y + 4 = - 23(x + 3)
  2. x - 3 = - 23(y - 4)
  3. y = - 23x + 7
  4. y - 4 = - 23(x - 3)

Answer: D) y - 4 = - 23(x - 3)

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

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88. The midpoint of AB is (2, 5) and A = (2, 1). The segment AB is:

  1. slanting downward
  2. horizontal
  3. slanting upward
  4. vertical

Answer: D) vertical

Explanation: B = (2, 9); A and B have the same x-coordinate. SLO M-09-B-02 · Knowledge

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89. Find k if the line kx + 2y = 5 is parallel to y = 3x + 1.

  1. k = 6
  2. k = - 23
  3. k = -6
  4. k = 23

Answer: C) k = -6

Explanation: Slope of kx + 2y = 5 is - k2. Setting - k2 = 3 gives k = -6. SLO M-09-B-05 · Understanding

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90. Find the equation of the line with slope -3 passing through (2, -1).

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

Answer: D) y = -3x + 5

Explanation: -1 = -3(2) + c Rightarrow c = 5, so y = -3x + 5. SLO M-09-B-04 · Knowledge

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91. Find k if the line y = kx - 1 is perpendicular to y = 4x + 3.

  1. k = -4
  2. k = 14
  3. k = - 14
  4. k = 4

Answer: C) k = - 14

Explanation: 4k = -1 Rightarrow k = - 14. SLO M-09-B-05 · Understanding

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92. The equation of the line with slope 0 and y-intercept 6 is:

  1. y = -6
  2. x = 6
  3. y = 6x
  4. y = 6

Answer: D) y = 6

Explanation: Put m = 0 and c = 6 into y = mx + c. SLO M-09-B-04 · Knowledge

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93. Find the gradient (slope) of the line through (2, 8) and (4, 1).

  1. 72
  2. 27
  3. - 72
  4. - 27

Answer: C) - 72

Explanation: m = y2 - y1x2 - x1 = 1 - 84 - 2 = -72 = - 72. SLO M-09-B-03 · Knowledge

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94. Find the equation of the line with slope 12 passing through (4, 0).

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

Answer: C) y = 12x - 2

Explanation: 0 = 12(4) + c Rightarrow c = -2, so y = 12x - 2. SLO M-09-B-04 · Knowledge

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95. Two friends live at (-4, 1) and (6, -7) on a town grid. They meet exactly halfway. The meeting point is:

  1. (5, -4)
  2. (1, -3)
  3. (10, -8)
  4. (-3, 1)

Answer: B) (1, -3)

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

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96. On a map grid where 1 unit = 5 km, Lahore is at (-3, 3) and Kasur is at (3, 11). The straight-line distance between them is:

  1. 50 km
  2. 70 km
  3. 100 km
  4. 10 km

Answer: A) 50 km

Explanation: Grid distance = 6^2 + 8^2 = 10 units = 10 5 = 50 km. SLO M-09-B-06 · Application

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97. The Earth turns 15^circ of longitude per hour. Pakistan's standard time meridian is 75^circE, so Pakistan's time is GMT plus:

  1. 7.5 hours
  2. 5 hours
  3. 6 hours
  4. 4 hours

Answer: B) 5 hours

Explanation: 75 div 15 = 5 hours. SLO M-09-B-07 · Application

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98. A rectangular field has corners (0, 0), (40, 0), (40, 30) and (0, 30) (metres). A straight path runs from (0, 0) to (40, 30). Its length is:

  1. 70 m
  2. 35 m
  3. 50 m
  4. 140 m

Answer: C) 50 m

Explanation: 40^2 + 30^2 = 2500 = 50 m. SLO M-09-B-06 · Application

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99. On a map grid where 1 unit = 5 km, Multan is at (5, 5) and Bahawalpur is at (10, 17). The straight-line distance between them is:

  1. 130 km
  2. 65 km
  3. 13 km
  4. 85 km

Answer: B) 65 km

Explanation: Grid distance = 5^2 + 12^2 = 13 units = 13 5 = 65 km. SLO M-09-B-06 · Application

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100. For the line y = -5x, the slope and y-intercept are:

  1. m = -5, c = 1
  2. m = -5, c = 0
  3. m = 5, c = 0
  4. m = 0, c = -5

Answer: B) m = -5, c = 0

Explanation: Compare with y = mx + c: m = -5 and c = 0. SLO M-09-B-04 · Knowledge

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