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9th Grade Coordinates: Quadrants, Midpoints and Distance Worksheet — Level 3 — Practice Set 2 — Answers

Answer sheet with worked solutions for the 9th Grade geometry worksheet.

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9th Grade Coordinates: Quadrants, Midpoints and Distance Worksheet — Level 3 — Practice Set 2 — 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 (3, 2) and (8, 8).

Answer: (5.5, 5)

  1. x: (3 + 8) ÷ 2 = 5.5
  2. y: (2 + 8) ÷ 2 = 5
2.Find the distance between (−3, 5) and (5, −10).

Answer: 17

  1. Horizontal change = 8, vertical change = 15
  2. d = √(82 + 152) = √289
  3. = 17
3.Find the distance between (4, −5) and (1, −14), correct to 1 decimal place.

Answer: 9.5

  1. Horizontal change = 3, vertical change = 9
  2. d = √(32 + 92) = √90
  3. = 9.5
4.Find the midpoint of the segment joining (−5, −9) and (−5, 6).

Answer: (−5, −1.5)

  1. x: (−5 + (−5)) ÷ 2 = −5
  2. y: (−9 + 6) ÷ 2 = −1.5
5.Find the midpoint of the segment joining (8, 0) and (−5, 4).

Answer: (1.5, 2)

  1. x: (8 + (−5)) ÷ 2 = 1.5
  2. y: (0 + 4) ÷ 2 = 2
6.Find the distance between (6, −3) and (4, −4), correct to 1 decimal place.

Answer: 2.2

  1. Horizontal change = 2, vertical change = 1
  2. d = √(22 + 12) = √5
  3. = 2.2
7.Find the midpoint of the segment joining (−1, 9) and (3, 5).

Answer: (1, 7)

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

Answer: 5.1

  1. Horizontal change = 1, vertical change = 5
  2. d = √(12 + 52) = √26
  3. = 5.1
9.Find the midpoint of the segment joining (5, −9) and (7, 9).

Answer: (6, 0)

  1. x: (5 + 7) ÷ 2 = 6
  2. y: (−9 + 9) ÷ 2 = 0
10.Find the distance between (−1, 4) and (4, 16).

Answer: 13

  1. Horizontal change = 5, vertical change = 12
  2. d = √(52 + 122) = √169
  3. = 13
11.Find the distance between (−4, −6) and (−9, 6).

Answer: 13

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

Answer: 15

  1. Horizontal change = 9, vertical change = 12
  2. d = √(92 + 122) = √225
  3. = 15
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