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Year 9 Coordinates: Quadrants, Midpoints and Distance Worksheet — Level 3 — Answers

Answer sheet with worked solutions for the Year 9 geometry worksheet.

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Success TutoringWorksheetsAnswer sheetYear 9 · Mathematics · Geometry

Year 9 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 (0, −4) and (2, 6).

Answer: (1, 1)

  1. x: (0 + 2) ÷ 2 = 1
  2. y: (−4 + 6) ÷ 2 = 1
2.Find the distance between (2, −3) and (7, 9).

Answer: 13

  1. Horizontal change = 5, vertical change = 12
  2. d = √(52 + 122) = √169
  3. = 13
3.Find the midpoint of the segment joining (−4, 6) and (0, −3).

Answer: (−2, 1.5)

  1. x: (−4 + 0) ÷ 2 = −2
  2. y: (6 + (−3)) ÷ 2 = 1.5
4.Find the distance between (2, 4) and (7, −8).

Answer: 13

  1. Horizontal change = 5, vertical change = 12
  2. d = √(52 + 122) = √169
  3. = 13
5.Find the distance between (−6, 6) and (2, 21).

Answer: 17

  1. Horizontal change = 8, vertical change = 15
  2. d = √(82 + 152) = √289
  3. = 17
6.Find the midpoint of the segment joining (4, 9) and (3, 0).

Answer: (3.5, 4.5)

  1. x: (4 + 3) ÷ 2 = 3.5
  2. y: (9 + 0) ÷ 2 = 4.5
7.Find the distance between (−5, −2) and (4, −14).

Answer: 15

  1. Horizontal change = 9, vertical change = 12
  2. d = √(92 + 122) = √225
  3. = 15
8.Find the distance between (2, 0) and (−4, 8).

Answer: 10

  1. Horizontal change = 6, vertical change = 8
  2. d = √(62 + 82) = √100
  3. = 10
9.Find the midpoint of the segment joining (−4, 4) and (1, 0).

Answer: (−1.5, 2)

  1. x: (−4 + 1) ÷ 2 = −1.5
  2. y: (4 + 0) ÷ 2 = 2
10.Find the distance between (−1, 5) and (2, 9).

Answer: 5

  1. Horizontal change = 3, vertical change = 4
  2. d = √(32 + 42) = √25
  3. = 5
11.Find the midpoint of the segment joining (0, −4) and (−7, −4).

Answer: (−3.5, −4)

  1. x: (0 + (−7)) ÷ 2 = −3.5
  2. y: (−4 + (−4)) ÷ 2 = −4
12.Find the distance between (−6, 0) and (−3, −1), correct to 1 decimal place.

Answer: 3.2

  1. Horizontal change = 3, vertical change = 1
  2. d = √(32 + 12) = √10
  3. = 3.2
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