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Coordinate Geometry MCQs — Mathematics (page 7)

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.

151. Find the distance between (5, -2) and (7, -6).

  1. 6
  2. 34
  3. 2 6
  4. 2 5

Answer: D) 2 5

Explanation: d = 2^2 + 4^2 = 20 = 2 5. SLO M-09-B-01 · Understanding

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152. The line x = 4 written in general form is:

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

Answer: B) x - 4 = 0

Explanation: Here a = 1, b = 0, c = -4; it is a vertical line. SLO M-09-B-09 · Understanding

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153. Find the midpoint of the segment joining (3, -9) and (7, 5).

  1. (2, 7)
  2. (-2, 5)
  3. (10, -4)
  4. (5, -2)

Answer: D) (5, -2)

Explanation: M = ( x1 + x22, y1 + y22 ) = ( 102, -42 ) = (5, -2). SLO M-09-B-02 · Knowledge

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154. A ship at (2, 3) moves in a straight line to (10, 9). At the halfway point it stops to refuel. The refuelling point is:

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

Answer: B) (6, 6)

Explanation: Midpoint = (6, 6). SLO M-09-B-07 · Application

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155. Using the two-point form, the equation of the line through (0, -3) and (4, 5) is:

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

Answer: B) y = 2x - 3

Explanation: y - y1y2 - y1 = x - x1x2 - x1 gives slope 2 and y = 2x - 3. SLO M-09-B-08 · Understanding

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156. M(6, -6) is the midpoint of AB and A = (0, -3). Find B.

  1. (3, - 92)
  2. (6, -3)
  3. (12, -9)
  4. (12, -15)

Answer: C) (12, -9)

Explanation: x2 = 2(6) - (0) = 12 and y2 = 2(-6) - (-3) = -9, so B = (12, -9). SLO M-09-B-02 · Knowledge

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157. Write 3x + 4y - 12 = 0 in intercept form.

  1. x4 + y3 = 1
  2. x3 + y4 = 1
  3. x4 - y3 = 1
  4. x-4 + y-3 = 1

Answer: A) x4 + y3 = 1

Explanation: 3x + 4y = 12; divide by 12: x4 + y3 = 1. SLO M-09-B-09 · Understanding

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158. The equation of the line with slope 2 and y-intercept 5 is:

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

Answer: C) y = 2x + 5

Explanation: Put m = 2 and c = 5 into y = mx + c. SLO M-09-B-04 · Knowledge

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159. In point-slope form, the line with slope -1 through (-2, 5) is:

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

Answer: C) y - 5 = -(x + 2)

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

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160. Using the two-point form, the equation of the line through (-1, 4) and (2, -2) is:

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

Answer: D) y = -2x + 2

Explanation: y - y1y2 - y1 = x - x1x2 - x1 gives slope -2 and y = -2x + 2. SLO M-09-B-08 · Understanding

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161. Find the gradient (slope) of the line through (6, 0) and (-3, 3).

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

Answer: A) - 13

Explanation: m = y2 - y1x2 - x1 = 3 - 0-3 - 6 = 3-9 = - 13. SLO M-09-B-03 · Knowledge

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162. A triangular park has corners (0, 0), (12, 0) and (12, 5) (metres). Fencing it costs Rs. 200 per metre. The total cost is:

  1. Rs. 12,000
  2. Rs. 6,000
  3. Rs. 5,800
  4. Rs. 3,400

Answer: B) Rs. 6,000

Explanation: Sides 12, 5 and 12^2 + 5^2 = 13; perimeter = 30 m; cost = 30 200 = 6000. SLO M-09-B-06 · Application

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163. Two towns lie on the same meridian, 8^circ of latitude apart. If 1^circ of latitude approx 111 km, the distance between them is about:

  1. 480 km
  2. 119 km
  3. 888 km
  4. 800 km

Answer: C) 888 km

Explanation: 8 111 = 888 km. SLO M-09-B-07 · Application

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164. Find the distance between A(0, 4) and B(-3, 8).

  1. 31
  2. 6
  3. 5
  4. 7

Answer: C) 5

Explanation: AB = (x2 - x1)^2 + (y2 - y1)^2 = 3^2 + 4^2 = 25 = 5. SLO M-09-B-01 · Understanding

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165. On a city grid map, a taxi can only drive along streets (horizontal and vertical). From (1, 2) to (5, 5) the shortest driving distance is:

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

Answer: B) 7 blocks

Explanation: It must drive 4 blocks across and 3 blocks up: 4 + 3 = 7. (The straight-line distance would be 5.) SLO M-09-B-07 · Application

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166. Find the midpoint of the segment joining (1, 6) and (-9, 1).

  1. ( 72, -4)
  2. (-4, 72)
  3. (-8, 7)
  4. (-5, - 52)

Answer: B) (-4, 72)

Explanation: M = ( x1 + x22, y1 + y22 ) = ( -82, 72 ) = (-4, 72). SLO M-09-B-02 · Knowledge

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167. The equation xcos 30^circ + ysin 30^circ = 6 is written in:

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

Answer: B) normal form

Explanation: xcos 30^circ + ysin 30^circ = 6 is the normal form. SLO M-09-B-08 · Understanding

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168. The equation x - 1cos 45^circ = y - 2sin 45^circ is written in:

  1. slope-intercept form
  2. two-point form
  3. symmetric form
  4. intercepts form

Answer: C) symmetric form

Explanation: x - 1cos 45^circ = y - 2sin 45^circ is the symmetric form. SLO M-09-B-08 · Understanding

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169. The end points of a diameter of a circle are (-2, 3) and (6, -5). The centre of the circle is:

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

Answer: D) (2, -1)

Explanation: The centre is the midpoint of the diameter: (2, -1). SLO M-09-B-02 · Knowledge

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170. Find the midpoint of the segment joining (2, -1) and (9, 7).

  1. (11, 6)
  2. ( 72, 4)
  3. (3, 112)
  4. ( 112, 3)

Answer: D) ( 112, 3)

Explanation: M = ( x1 + x22, y1 + y22 ) = ( 112, 62 ) = ( 112, 3). SLO M-09-B-02 · Knowledge

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171. A line is parallel to a line of slope -1. Its slope is:

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

Answer: C) -1

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

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172. M(4, 0) is the midpoint of AB and A = (-3, 2). Find B.

  1. ( 12, 1)
  2. (5, 2)
  3. (7, -2)
  4. (11, -2)

Answer: D) (11, -2)

Explanation: x2 = 2(4) - (-3) = 11 and y2 = 2(0) - (2) = -2, so B = (11, -2). SLO M-09-B-02 · Knowledge

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173. Find the gradient (slope) of the line through (8, 6) and (-3, 5).

  1. - 111
  2. 11
  3. -11
  4. 111

Answer: D) 111

Explanation: m = y2 - y1x2 - x1 = 5 - 6-3 - 8 = -1-11 = 111. SLO M-09-B-03 · Knowledge

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174. For the line 6x + 3y + 9 = 0, the slope is:

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

Answer: B) -2

Explanation: m = - ab = - 63 = -2. SLO M-09-B-09 · Understanding

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175. The points A(1, 1), B(3, 5) and C(5, 9) are collinear because:

  1. they have positive coordinates
  2. AB = BC
  3. mAB = mBC = 2
  4. mAB mBC = -1

Answer: C) mAB = mBC = 2

Explanation: mAB = 5 - 13 - 1 = 2 and mBC = 9 - 55 - 3 = 2; equal slopes through the common point B mean one straight line. SLO M-09-B-05 · Understanding

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