MCQs / Mathematics / Coordinate Geometry

Coordinate Geometry MCQs — Mathematics (page 8)

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.

176. The line through (0, -1) and (3, k) has slope 53. Find k.

  1. -4
  2. 4
  3. 5
  4. 23

Answer: B) 4

Explanation: k - (-1)3 - 0 = 53 Rightarrow k = -1 + 53 3 = 4. SLO M-09-B-03 · Knowledge

Discuss this question

177. The line cuts the x-axis at 3 and the y-axis at 4. In intercept form its equation is:

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

Answer: D) x3 + y4 = 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

Discuss this question

178. If the distance between (1, 2) and (4, k) is 5, the possible values of k are:

  1. 6 or -2
  2. 6 only
  3. 4 or -4
  4. -6 or 2

Answer: A) 6 or -2

Explanation: (4 - 1)^2 + (k - 2)^2 = 25 Rightarrow (k - 2)^2 = 16 Rightarrow k - 2 = pm 4 Rightarrow k = 6 or -2. SLO M-09-B-01 · Understanding

Discuss this question

179. A road rises 12 m over a horizontal distance of 200 m. Its gradient is:

  1. 6
  2. 0.6
  3. 0.06
  4. 16.7

Answer: C) 0.06

Explanation: 12200 = 0.06, i.e. a 6% gradient. SLO M-09-B-03 · Knowledge

Discuss this question

180. Find the gradient (slope) of the line through (-5, 2) and (-8, 5).

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

Answer: D) -1

Explanation: m = y2 - y1x2 - x1 = 5 - 2-8 - (-5) = 3-3 = -1. SLO M-09-B-03 · Knowledge

Discuss this question

181. A plane takes off along the line y = 14x (x = horizontal km, y = height km). After 8 km horizontally its height is:

  1. 4 km
  2. 2 km
  3. 0.5 km
  4. 32 km

Answer: B) 2 km

Explanation: y = 14(8) = 2 km. SLO M-09-B-07 · Application

Discuss this question

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

  1. (0, -5)
  2. (-10, 0)
  3. (-5, 0)
  4. (2, -9)

Answer: C) (-5, 0)

Explanation: M = ( x1 + x22, y1 + y22 ) = ( -102, 02 ) = (-5, 0). SLO M-09-B-02 · Knowledge

Discuss this question

183. Find the midpoint of the segment joining (-8, -7) and (-1, -1).

  1. (-9, -8)
  2. ( 72, 3)
  3. (- 92, -4)
  4. (-4, - 92)

Answer: C) (- 92, -4)

Explanation: M = ( x1 + x22, y1 + y22 ) = ( -92, -82 ) = (- 92, -4). SLO M-09-B-02 · Knowledge

Discuss this question

184. The normal form of the line whose perpendicular from the origin has length 3 and makes an angle of 45^circ with the x-axis is:

  1. xsin 45^circ + ycos 45^circ = 3
  2. xcos 45^circ + ysin 45^circ = 3
  3. xcos 45^circ + ysin 45^circ = 9
  4. xcos 45^circ - ysin 45^circ = 3

Answer: B) xcos 45^circ + ysin 45^circ = 3

Explanation: Normal form: xcosalpha + ysinalpha = p. Here this is x ( 1 2 ) + y ( 1 2 ) = 3. SLO M-09-B-08 · Understanding

Discuss this question

185. Find the distance between A(-2, 0) and B(7, -12).

  1. 15
  2. 9 3
  3. 21
  4. 16

Answer: A) 15

Explanation: AB = (x2 - x1)^2 + (y2 - y1)^2 = 9^2 + 12^2 = 225 = 15. SLO M-09-B-01 · Understanding

Discuss this question

186. A circular garden has its centre at (3, 4) and a tree on its edge at (6, 8) (metres). The radius of the garden is:

  1. 3 m
  2. 7 m
  3. 25 m
  4. 5 m

Answer: D) 5 m

Explanation: r = 3^2 + 4^2 = 5 m. SLO M-09-B-06 · Application

Discuss this question

187. A rescue boat at (0, 0) must reach a swimmer at (9, 12) (metres) in a straight line. How far must it travel?

  1. 12 m
  2. 225 m
  3. 15 m
  4. 21 m

Answer: C) 15 m

Explanation: 81 + 144 = 15 m. SLO M-09-B-06 · Application

Discuss this question

188. The slope of the line through (a, b) and (2a, 3b) (with a neq 0) is:

  1. 3b2a
  2. 2ab
  3. a2b
  4. 2ba

Answer: D) 2ba

Explanation: 3b - b2a - a = 2ba. SLO M-09-B-03 · Knowledge

Discuss this question

189. The equation y - 3 = 2(x + 1) is written in:

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

Answer: D) point-slope form

Explanation: y - 3 = 2(x + 1) is the point-slope form. SLO M-09-B-08 · Understanding

Discuss this question

190. The line through (1, 3) and (4, k) has slope 2. Find k.

  1. 9
  2. -9
  3. 5
  4. 10

Answer: A) 9

Explanation: k - 34 - 1 = 2 Rightarrow k = 3 + 2 3 = 9. SLO M-09-B-03 · Knowledge

Discuss this question

191. In point-slope form, the line with slope 3 through (2, -1) is:

  1. y = 3x - 6
  2. x - 2 = 3(y + 1)
  3. y + 1 = 3(x - 2)
  4. y - 1 = 3(x + 2)

Answer: C) y + 1 = 3(x - 2)

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

Discuss this question

192. A line is perpendicular to a line of slope -6. Its slope is:

  1. 16
  2. 6
  3. - 16
  4. -6

Answer: A) 16

Explanation: Perpendicular slopes multiply to -1: m2 = - 1-6 = 16. SLO M-09-B-05 · Understanding

Discuss this question

193. If c = 0 in ax + by + c = 0, the line:

  1. passes through the origin
  2. is vertical
  3. is horizontal
  4. has slope zero

Answer: A) passes through the origin

Explanation: (0, 0) satisfies ax + by = 0. SLO M-09-B-09 · Understanding

Discuss this question

194. Find the midpoint of the segment joining (-5, 4) and (8, -4).

  1. ( 132, -4)
  2. ( 32, 0)
  3. (3, 0)
  4. (0, 32)

Answer: B) ( 32, 0)

Explanation: M = ( x1 + x22, y1 + y22 ) = ( 32, 02 ) = ( 32, 0). SLO M-09-B-02 · Knowledge

Discuss this question

195. For the line y = - 12x + 4, the slope and y-intercept are:

  1. m = - 12, c = 4
  2. m = - 12, c = -4
  3. m = 4, c = - 12
  4. m = 12, c = 4

Answer: A) m = - 12, c = 4

Explanation: Compare with y = mx + c: m = - 12 and c = 4. SLO M-09-B-04 · Knowledge

Discuss this question

Previous Page 8 of 8

Practise Coordinate Geometry MCQs

More Mathematics chapters