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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 (−6, 8) and (2, −4).

Answer: (−2, 2)

  1. x: (−6 + 2) ÷ 2 = −2
  2. y: (8 + (−4)) ÷ 2 = 2
2.Find the distance between (−4, 5) and (1, −7).

Answer: 13

  1. Horizontal change = 5, vertical change = 12
  2. d = √(52 + 122) = √169
  3. = 13
3.Find the midpoint of the segment joining (2, 6) and (4, 9).

Answer: (3, 7.5)

  1. x: (2 + 4) ÷ 2 = 3
  2. y: (6 + 9) ÷ 2 = 7.5
4.Find the midpoint of the segment joining (2, −7) and (0, 3).

Answer: (1, −2)

  1. x: (2 + 0) ÷ 2 = 1
  2. y: (−7 + 3) ÷ 2 = −2
5.Find the distance between (−4, 0) and (−12, −9), correct to 1 decimal place.

Answer: 12.0

  1. Horizontal change = 8, vertical change = 9
  2. d = √(82 + 92) = √145
  3. = 12.0
6.Find the midpoint of the segment joining (−1, 0) and (−4, 5).

Answer: (−2.5, 2.5)

  1. x: (−1 + (−4)) ÷ 2 = −2.5
  2. y: (0 + 5) ÷ 2 = 2.5
7.Find the distance between (2, 6) and (3, −3), correct to 1 decimal place.

Answer: 9.1

  1. Horizontal change = 1, vertical change = 9
  2. d = √(12 + 92) = √82
  3. = 9.1
8.Find the midpoint of the segment joining (4, −3) and (−1, 7).

Answer: (1.5, 2)

  1. x: (4 + (−1)) ÷ 2 = 1.5
  2. y: (−3 + 7) ÷ 2 = 2
9.Find the distance between (6, −4) and (11, 8).

Answer: 13

  1. Horizontal change = 5, vertical change = 12
  2. d = √(52 + 122) = √169
  3. = 13
10.Find the distance between (−2, −1) and (−7, −13).

Answer: 13

  1. Horizontal change = 5, vertical change = 12
  2. d = √(52 + 122) = √169
  3. = 13
11.Find the midpoint of the segment joining (−1, −7) and (4, 8).

Answer: (1.5, 0.5)

  1. x: (−1 + 4) ÷ 2 = 1.5
  2. y: (−7 + 8) ÷ 2 = 0.5
12.Find the midpoint of the segment joining (−9, −2) and (3, 4).

Answer: (−3, 1)

  1. x: (−9 + 3) ÷ 2 = −3
  2. y: (−2 + 4) ÷ 2 = 1
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