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

Answer sheet with worked solutions for the 10th Grade geometry worksheet.

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10th Grade 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 distance between (1, −5) and (−5, 3).

Answer: 10

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

Answer: (4.5, −4)

  1. x: (3 + 6) ÷ 2 = 4.5
  2. y: (−9 + 1) ÷ 2 = −4
3.Find the distance between (2, 3) and (8, −5).

Answer: 10

  1. Horizontal change = 6, vertical change = 8
  2. d = √(62 + 82) = √100
  3. = 10
4.Find the distance between (6, 1) and (15, 13).

Answer: 15

  1. Horizontal change = 9, vertical change = 12
  2. d = √(92 + 122) = √225
  3. = 15
5.Find the midpoint of the segment joining (9, 0) and (−1, −1).

Answer: (4, −0.5)

  1. x: (9 + (−1)) ÷ 2 = 4
  2. y: (0 + (−1)) ÷ 2 = −0.5
6.Find the distance between (3, 1) and (−2, −1), correct to 1 decimal place.

Answer: 5.4

  1. Horizontal change = 5, vertical change = 2
  2. d = √(52 + 22) = √29
  3. = 5.4
7.Find the midpoint of the segment joining (−9, −7) and (3, −3).

Answer: (−3, −5)

  1. x: (−9 + 3) ÷ 2 = −3
  2. y: (−7 + (−3)) ÷ 2 = −5
8.Find the midpoint of the segment joining (−6, −5) and (8, −5).

Answer: (1, −5)

  1. x: (−6 + 8) ÷ 2 = 1
  2. y: (−5 + (−5)) ÷ 2 = −5
9.Find the distance between (5, −3) and (13, −18).

Answer: 17

  1. Horizontal change = 8, vertical change = 15
  2. d = √(82 + 152) = √289
  3. = 17
10.Find the distance between (−5, −3) and (−11, −11).

Answer: 10

  1. Horizontal change = 6, vertical change = 8
  2. d = √(62 + 82) = √100
  3. = 10
11.Find the distance between (−5, 5) and (0, −4), correct to 1 decimal place.

Answer: 10.3

  1. Horizontal change = 5, vertical change = 9
  2. d = √(52 + 92) = √106
  3. = 10.3
12.Find the midpoint of the segment joining (8, 3) and (−2, −7).

Answer: (3, −2)

  1. x: (8 + (−2)) ÷ 2 = 3
  2. y: (3 + (−7)) ÷ 2 = −2
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