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Year 7 Coordinates: Quadrants, Midpoints and Distance Worksheet — Level 3 — Practice Set 4 — Answers

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Year 7 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 (5, −2) and (−5, −7).

Answer: (0, −4.5)

  1. x: (5 + (−5)) ÷ 2 = 0
  2. y: (−2 + (−7)) ÷ 2 = −4.5
2.Find the distance between (4, −1) and (0, −9), correct to 1 decimal place.

Answer: 8.9

  1. Horizontal change = 4, vertical change = 8
  2. d = √(42 + 82) = √80
  3. = 8.9
3.Find the midpoint of the segment joining (5, 8) and (−3, −5).

Answer: (1, 1.5)

  1. x: (5 + (−3)) ÷ 2 = 1
  2. y: (8 + (−5)) ÷ 2 = 1.5
4.Find the midpoint of the segment joining (1, 0) and (−7, −6).

Answer: (−3, −3)

  1. x: (1 + (−7)) ÷ 2 = −3
  2. y: (0 + (−6)) ÷ 2 = −3
5.Find the distance between (3, −6) and (12, −15), correct to 1 decimal place.

Answer: 12.7

  1. Horizontal change = 9, vertical change = 9
  2. d = √(92 + 92) = √162
  3. = 12.7
6.Find the midpoint of the segment joining (−9, −2) and (−1, 3).

Answer: (−5, 0.5)

  1. x: (−9 + (−1)) ÷ 2 = −5
  2. y: (−2 + 3) ÷ 2 = 0.5
7.Find the midpoint of the segment joining (3, 0) and (7, 8).

Answer: (5, 4)

  1. x: (3 + 7) ÷ 2 = 5
  2. y: (0 + 8) ÷ 2 = 4
8.Find the distance between (6, −4) and (3, 3), correct to 1 decimal place.

Answer: 7.6

  1. Horizontal change = 3, vertical change = 7
  2. d = √(32 + 72) = √58
  3. = 7.6
9.Find the distance between (4, 4) and (9, 10), correct to 1 decimal place.

Answer: 7.8

  1. Horizontal change = 5, vertical change = 6
  2. d = √(52 + 62) = √61
  3. = 7.8
10.Find the distance between (2, 2) and (11, 4), correct to 1 decimal place.

Answer: 9.2

  1. Horizontal change = 9, vertical change = 2
  2. d = √(92 + 22) = √85
  3. = 9.2
11.Find the distance between (6, 6) and (−2, 8), correct to 1 decimal place.

Answer: 8.2

  1. Horizontal change = 8, vertical change = 2
  2. d = √(82 + 22) = √68
  3. = 8.2
12.Find the midpoint of the segment joining (−5, −2) and (−4, 3).

Answer: (−4.5, 0.5)

  1. x: (−5 + (−4)) ÷ 2 = −4.5
  2. y: (−2 + 3) ÷ 2 = 0.5
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