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Coordinate Geometry MCQs — Mathematics (page 6)

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.

126. Using the distance formula, the triangle with vertices (0, 0), (6, 0) and (3, 4) is:

  1. isosceles
  2. right-angled
  3. scalene
  4. equilateral

Answer: A) isosceles

Explanation: Sides: 6, 3^2 + 4^2 = 5 and 3^2 + 4^2 = 5; two sides are equal. SLO M-09-B-01 · Understanding

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127. Write 3x + 4y = 12 in the form y = mx + c.

  1. y = - 43x + 3
  2. y = 34x + 3
  3. y = 34x - 3
  4. y = - 34x + 3

Answer: D) y = - 34x + 3

Explanation: 4y = -3x + 12 Rightarrow y = - 34x + 3. SLO M-09-B-04 · Knowledge

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128. Write 4x + 6y + 24 = 0 in intercept form.

  1. x-6 + y-4 = 1
  2. x-4 + y-6 = 1
  3. x4 + y6 = 1
  4. x6 + y4 = 1

Answer: A) x-6 + y-4 = 1

Explanation: 4x + 6y = -24; divide by -24: x-6 + y-4 = 1. SLO M-09-B-09 · Understanding

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129. Find the midpoint of the segment joining (6, -4) and (9, 7).

  1. ( 32, 112)
  2. (15, 3)
  3. ( 152, 32)
  4. ( 32, 152)

Answer: C) ( 152, 32)

Explanation: M = ( x1 + x22, y1 + y22 ) = ( 152, 32 ) = ( 152, 32). SLO M-09-B-02 · Knowledge

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130. The line through (-2, 5) and (2, k) has slope - 34. Find k.

  1. 3
  2. 174
  3. 2
  4. -2

Answer: C) 2

Explanation: k - 52 - (-2) = - 34 Rightarrow k = 5 + - 34 4 = 2. SLO M-09-B-03 · Knowledge

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131. The slope of the line through (2, 2) and (7, 7) is:

  1. 1
  2. 7
  3. -1
  4. 0

Answer: A) 1

Explanation: 7 - 27 - 2 = 1 (the line y = x). SLO M-09-B-03 · Knowledge

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132. The equation of the line through (1, 2) perpendicular to y = 2x + 7 is:

  1. y = - 12x + 52
  2. y = 2x
  3. y = 12x + 32
  4. y = -2x + 4

Answer: A) y = - 12x + 52

Explanation: Slope - 12; 2 = - 12(1) + c Rightarrow c = 52. SLO M-09-B-05 · Understanding

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133. For the line 4x - 5y + 20 = 0, the slope is:

  1. - 45
  2. - 54
  3. 54
  4. 45

Answer: D) 45

Explanation: m = - ab = - 4-5 = 45. SLO M-09-B-09 · Understanding

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134. Find the distance between A(4, 3) and B(10, 11).

  1. 11
  2. 10
  3. 14
  4. 4 7

Answer: B) 10

Explanation: AB = (x2 - x1)^2 + (y2 - y1)^2 = 6^2 + 8^2 = 100 = 10. SLO M-09-B-01 · Understanding

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135. A line is parallel to a line of slope 3. Its slope is:

  1. - 600479950316066118014398509481984
  2. 3
  3. 600479950316066118014398509481984
  4. -3

Answer: B) 3

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

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136. The distance of the point (-5, 12) from the origin is:

  1. 14
  2. 13
  3. 17
  4. 15

Answer: B) 13

Explanation: (-5)^2 + 12^2 = 13. SLO M-09-B-01 · Understanding

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137. A ship sails from port P(-2, -3) to island I(4, 5), with 1 unit = 10 nautical miles. The distance sailed is:

  1. 10 nautical miles
  2. 50 nautical miles
  3. 140 nautical miles
  4. 100 nautical miles

Answer: D) 100 nautical miles

Explanation: 6^2 + 8^2 = 10 units = 100 nautical miles. SLO M-09-B-06 · Application

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138. The line cuts the x-axis at 6 and the y-axis at -3. In intercept form its equation is:

  1. x-3 + y6 = 1
  2. x6 - y-3 = 1
  3. x6 + y-3 = 1
  4. 6x - 3y = 1

Answer: C) x6 + y-3 = 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

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139. The line cuts the x-axis at -2 and the y-axis at 5. In intercept form its equation is:

  1. x-2 - y5 = 1
  2. x-2 + y5 = 1
  3. -2x + 5y = 1
  4. x5 + y-2 = 1

Answer: B) x-2 + y5 = 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

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140. Find the gradient (slope) of the line through (-1, -8) and (-7, 4).

  1. -2
  2. 2
  3. 12
  4. - 12

Answer: A) -2

Explanation: m = y2 - y1x2 - x1 = 4 - (-8)-7 - (-1) = 12-6 = -2. SLO M-09-B-03 · Knowledge

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141. Which point lies on y = 3x - 4?

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

Answer: B) (2, 2)

Explanation: 3(2) - 4 = 2. ✓ SLO M-09-B-04 · Knowledge

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142. Find the distance between A(2, 1) and B(-7, -39).

  1. 41
  2. 1699
  3. 49
  4. 42

Answer: A) 41

Explanation: AB = (x2 - x1)^2 + (y2 - y1)^2 = 9^2 + 40^2 = 1681 = 41. SLO M-09-B-01 · Understanding

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143. The distance of the line 5x - 12y + 26 = 0 from the origin is:

  1. 2
  2. 26
  3. 13
  4. 2617

Answer: A) 2

Explanation: Normal form divides by 25 + 144 = 13: p = 2613 = 2. SLO M-09-B-09 · Understanding

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144. The lines 3x + 4y - 1 = 0 and 4x - 3y + 5 = 0 are:

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

Answer: D) perpendicular

Explanation: Slopes: m1 = - 34, m2 = 43. Their product is -1, so the lines are perpendicular. SLO M-09-B-05 · Understanding

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145. The equation y = 4x - 7 is written in:

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

Answer: D) slope-intercept form

Explanation: y = 4x - 7 is the slope-intercept form. SLO M-09-B-08 · Understanding

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146. Find the distance between (-4, 1) and (-1, -2).

  1. 6
  2. 22
  3. 34
  4. 3 2

Answer: D) 3 2

Explanation: d = 3^2 + 3^2 = 18 = 3 2. SLO M-09-B-01 · Understanding

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147. Find the distance between (0, -4) and (1, -9).

  1. 30
  2. 26
  3. 34
  4. 6

Answer: B) 26

Explanation: d = 1^2 + 5^2 = 26 = 26. SLO M-09-B-01 · Understanding

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148. The x- and y-intercepts of x + 4y - 8 = 0 are:

  1. -8 and -2
  2. -8 and -8
  3. 2 and 8
  4. 8 and 2

Answer: D) 8 and 2

Explanation: Put y = 0: x = 8. Put x = 0: y = 2. SLO M-09-B-09 · Understanding

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149. Two friends live at (0, 12) and (8, 0) on a town grid. They meet exactly halfway. The meeting point is:

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

Answer: C) (4, 6)

Explanation: Halfway is the midpoint: (4, 6). SLO M-09-B-06 · Application

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150. A line makes an angle of 45^circ with the positive x-axis. Its slope is:

  1. 1
  2. 0
  3. -1
  4. 3

Answer: A) 1

Explanation: m = tan 45^circ = 1. SLO M-09-B-03 · Knowledge

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