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Year 9 Coordinates: Quadrants, Midpoints and Distance Worksheet — Level 3 — Practice Set 4 — Answers

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Success TutoringWorksheetsAnswer sheetYear 9 · Mathematics · Geometry

Year 9 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 distance between (0, 1) and (−5, 13).

Answer: 13

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

Answer: (−2, −6)

  1. x: (−2 + (−2)) ÷ 2 = −2
  2. y: (−3 + (−9)) ÷ 2 = −6
4.Find the midpoint of the segment joining (−8, −2) and (−4, −3).

Answer: (−6, −2.5)

  1. x: (−8 + (−4)) ÷ 2 = −6
  2. y: (−2 + (−3)) ÷ 2 = −2.5
5.Find the midpoint of the segment joining (1, 5) and (0, 4).

Answer: (0.5, 4.5)

  1. x: (1 + 0) ÷ 2 = 0.5
  2. y: (5 + 4) ÷ 2 = 4.5
6.Find the distance between (−4, 0) and (−1, −4).

Answer: 5

  1. Horizontal change = 3, vertical change = 4
  2. d = √(32 + 42) = √25
  3. = 5
7.Find the midpoint of the segment joining (7, 6) and (−1, −5).

Answer: (3, 0.5)

  1. x: (7 + (−1)) ÷ 2 = 3
  2. y: (6 + (−5)) ÷ 2 = 0.5
8.Find the distance between (−5, 3) and (−10, −1), correct to 1 decimal place.

Answer: 6.4

  1. Horizontal change = 5, vertical change = 4
  2. d = √(52 + 42) = √41
  3. = 6.4
9.Find the distance between (6, −6) and (1, −14), correct to 1 decimal place.

Answer: 9.4

  1. Horizontal change = 5, vertical change = 8
  2. d = √(52 + 82) = √89
  3. = 9.4
10.Find the midpoint of the segment joining (7, 7) and (−8, −7).

Answer: (−0.5, 0)

  1. x: (7 + (−8)) ÷ 2 = −0.5
  2. y: (7 + (−7)) ÷ 2 = 0
11.Find the distance between (−2, −5) and (1, −1).

Answer: 5

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

Answer: (1.5, −1)

  1. x: (3 + 0) ÷ 2 = 1.5
  2. y: (−3 + 1) ÷ 2 = −1
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