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Year 10 Coordinates: Quadrants, Midpoints and Distance Worksheet — Level 3 — Practice Set 4 — Answers

Answer sheet with worked solutions for the Year 10 geometry worksheet.

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Year 10 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 (2, 2) and (4, −1).

Answer: (3, 0.5)

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

Answer: (3, −3)

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

Answer: (−5.5, −1)

  1. x: (−3 + (−8)) ÷ 2 = −5.5
  2. y: (−6 + 4) ÷ 2 = −1
4.Find the distance between (−3, 3) and (6, −9).

Answer: 15

  1. Horizontal change = 9, vertical change = 12
  2. d = √(92 + 122) = √225
  3. = 15
5.Find the midpoint of the segment joining (0, −2) and (2, 2).

Answer: (1, 0)

  1. x: (0 + 2) ÷ 2 = 1
  2. y: (−2 + 2) ÷ 2 = 0
6.Find the distance between (−5, −3) and (−13, −18).

Answer: 17

  1. Horizontal change = 8, vertical change = 15
  2. d = √(82 + 152) = √289
  3. = 17
7.Find the distance between (4, 3) and (12, −12).

Answer: 17

  1. Horizontal change = 8, vertical change = 15
  2. d = √(82 + 152) = √289
  3. = 17
8.Find the midpoint of the segment joining (6, 3) and (4, −7).

Answer: (5, −2)

  1. x: (6 + 4) ÷ 2 = 5
  2. y: (3 + (−7)) ÷ 2 = −2
9.Find the midpoint of the segment joining (6, −9) and (−6, 6).

Answer: (0, −1.5)

  1. x: (6 + (−6)) ÷ 2 = 0
  2. y: (−9 + 6) ÷ 2 = −1.5
10.Find the distance between (−5, −6) and (3, −3), correct to 1 decimal place.

Answer: 8.5

  1. Horizontal change = 8, vertical change = 3
  2. d = √(82 + 32) = √73
  3. = 8.5
11.Find the distance between (0, 2) and (7, 5), correct to 1 decimal place.

Answer: 7.6

  1. Horizontal change = 7, vertical change = 3
  2. d = √(72 + 32) = √58
  3. = 7.6
12.Find the midpoint of the segment joining (−6, −7) and (−5, 6).

Answer: (−5.5, −0.5)

  1. x: (−6 + (−5)) ÷ 2 = −5.5
  2. y: (−7 + 6) ÷ 2 = −0.5
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