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Year 11 Coordinates: Quadrants, Midpoints and Distance Worksheet — Level 3 — Practice Set 4 — Answers

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Year 11 Coordinates: Quadrants, Midpoints and Distance Worksheet — Level 3 — Practice Set 4 — Answers

Midpoint = (average of the x-values, average of the y-values). Distance: use Pythagoras with the horizontal and vertical changes.

1.Find the midpoint of the segment joining (−1, 7) and (−8, 9).

Answer: (−4.5, 8)

  1. x: (−1 + (−8)) ÷ 2 = −4.5
  2. y: (7 + 9) ÷ 2 = 8
2.Find the midpoint of the segment joining (−9, 5) and (−1, 5).

Answer: (−5, 5)

  1. x: (−9 + (−1)) ÷ 2 = −5
  2. y: (5 + 5) ÷ 2 = 5
3.Find the distance between (−6, 6) and (−15, 18).

Answer: 15

  1. Horizontal change = 9, vertical change = 12
  2. d = √(92 + 122) = √225
  3. = 15
4.Find the distance between (−5, −4) and (−13, −19).

Answer: 17

  1. Horizontal change = 8, vertical change = 15
  2. d = √(82 + 152) = √289
  3. = 17
5.Find the distance between (−5, −1) and (−14, −13).

Answer: 15

  1. Horizontal change = 9, vertical change = 12
  2. d = √(92 + 122) = √225
  3. = 15
6.Find the midpoint of the segment joining (−1, 3) and (−4, −4).

Answer: (−2.5, −0.5)

  1. x: (−1 + (−4)) ÷ 2 = −2.5
  2. y: (3 + (−4)) ÷ 2 = −0.5
7.Find the midpoint of the segment joining (−6, −6) and (4, 2).

Answer: (−1, −2)

  1. x: (−6 + 4) ÷ 2 = −1
  2. y: (−6 + 2) ÷ 2 = −2
8.Find the midpoint of the segment joining (4, 6) and (−4, 8).

Answer: (0, 7)

  1. x: (4 + (−4)) ÷ 2 = 0
  2. y: (6 + 8) ÷ 2 = 7
9.Find the midpoint of the segment joining (8, −2) and (−9, 2).

Answer: (−0.5, 0)

  1. x: (8 + (−9)) ÷ 2 = −0.5
  2. y: (−2 + 2) ÷ 2 = 0
10.Find the midpoint of the segment joining (3, −6) and (−9, −4).

Answer: (−3, −5)

  1. x: (3 + (−9)) ÷ 2 = −3
  2. y: (−6 + (−4)) ÷ 2 = −5
11.Find the distance between (1, −5) and (−2, −1).

Answer: 5

  1. Horizontal change = 3, vertical change = 4
  2. d = √(32 + 42) = √25
  3. = 5
12.Find the distance between (−2, −2) and (0, −1), correct to 1 decimal place.

Answer: 2.2

  1. Horizontal change = 2, vertical change = 1
  2. d = √(22 + 12) = √5
  3. = 2.2
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