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8th Grade Coordinates: Quadrants, Midpoints and Distance Worksheet — Level 3 — Answers

Answer sheet with worked solutions for the 8th Grade geometry worksheet.

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8th Grade Coordinates: Quadrants, Midpoints and Distance Worksheet — Level 3 — 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 (−7, 8) and (3, 2).

Answer: (−2, 5)

  1. x: (−7 + 3) ÷ 2 = −2
  2. y: (8 + 2) ÷ 2 = 5
2.Find the distance between (−6, 5) and (−11, −7).

Answer: 13

  1. Horizontal change = 5, vertical change = 12
  2. d = √(52 + 122) = √169
  3. = 13
3.Find the distance between (1, −3) and (7, −11).

Answer: 10

  1. Horizontal change = 6, vertical change = 8
  2. d = √(62 + 82) = √100
  3. = 10
4.Find the distance between (2, −2) and (−3, 10).

Answer: 13

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

Answer: (−2, −2.5)

  1. x: (−6 + 2) ÷ 2 = −2
  2. y: (−1 + (−4)) ÷ 2 = −2.5
6.Find the distance between (3, −4) and (12, −16).

Answer: 15

  1. Horizontal change = 9, vertical change = 12
  2. d = √(92 + 122) = √225
  3. = 15
7.Find the distance between (3, 1) and (−3, −5), correct to 1 decimal place.

Answer: 8.5

  1. Horizontal change = 6, vertical change = 6
  2. d = √(62 + 62) = √72
  3. = 8.5
8.Find the midpoint of the segment joining (9, −2) and (5, 5).

Answer: (7, 1.5)

  1. x: (9 + 5) ÷ 2 = 7
  2. y: (−2 + 5) ÷ 2 = 1.5
9.Find the midpoint of the segment joining (3, −2) and (2, 7).

Answer: (2.5, 2.5)

  1. x: (3 + 2) ÷ 2 = 2.5
  2. y: (−2 + 7) ÷ 2 = 2.5
10.Find the midpoint of the segment joining (−9, 7) and (−7, 6).

Answer: (−8, 6.5)

  1. x: (−9 + (−7)) ÷ 2 = −8
  2. y: (7 + 6) ÷ 2 = 6.5
11.Find the distance between (6, 2) and (1, −10).

Answer: 13

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

Answer: (−7, 2)

  1. x: (−5 + (−9)) ÷ 2 = −7
  2. y: (−5 + 9) ÷ 2 = 2
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