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10th Grade Coordinates: Quadrants, Midpoints and Distance Worksheet — Level 3 — Practice Set 3 — Answers

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10th Grade Coordinates: Quadrants, Midpoints and Distance Worksheet — Level 3 — Practice Set 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 (−1, 6) and (−5, −4).

Answer: (−3, 1)

  1. x: (−1 + (−5)) ÷ 2 = −3
  2. y: (6 + (−4)) ÷ 2 = 1
2.Find the distance between (−1, 1) and (−7, 9).

Answer: 10

  1. Horizontal change = 6, vertical change = 8
  2. d = √(62 + 82) = √100
  3. = 10
3.Find the midpoint of the segment joining (7, −6) and (−4, −2).

Answer: (1.5, −4)

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

Answer: 5.7

  1. Horizontal change = 4, vertical change = 4
  2. d = √(42 + 42) = √32
  3. = 5.7
5.Find the distance between (3, −1) and (9, −9).

Answer: 10

  1. Horizontal change = 6, vertical change = 8
  2. d = √(62 + 82) = √100
  3. = 10
6.Find the distance between (−6, 2) and (−9, −2).

Answer: 5

  1. Horizontal change = 3, vertical change = 4
  2. d = √(32 + 42) = √25
  3. = 5
7.Find the distance between (−1, 4) and (8, 16).

Answer: 15

  1. Horizontal change = 9, vertical change = 12
  2. d = √(92 + 122) = √225
  3. = 15
8.Find the midpoint of the segment joining (−6, −7) and (6, −6).

Answer: (0, −6.5)

  1. x: (−6 + 6) ÷ 2 = 0
  2. y: (−7 + (−6)) ÷ 2 = −6.5
9.Find the distance between (4, 4) and (−5, 0), correct to 1 decimal place.

Answer: 9.8

  1. Horizontal change = 9, vertical change = 4
  2. d = √(92 + 42) = √97
  3. = 9.8
10.Find the distance between (5, −2) and (6, −7), correct to 1 decimal place.

Answer: 5.1

  1. Horizontal change = 1, vertical change = 5
  2. d = √(12 + 52) = √26
  3. = 5.1
11.Find the distance between (2, −6) and (−4, −1), correct to 1 decimal place.

Answer: 7.8

  1. Horizontal change = 6, vertical change = 5
  2. d = √(62 + 52) = √61
  3. = 7.8
12.Find the midpoint of the segment joining (−7, 6) and (5, 4).

Answer: (−1, 5)

  1. x: (−7 + 5) ÷ 2 = −1
  2. y: (6 + 4) ÷ 2 = 5
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