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Year 11 Coordinates: Quadrants, Midpoints and Distance Worksheet — Level 3 — Practice Set 3 — Answers

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Year 11 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 (4, 0) and (2, 9).

Answer: (3, 4.5)

  1. x: (4 + 2) ÷ 2 = 3
  2. y: (0 + 9) ÷ 2 = 4.5
2.Find the midpoint of the segment joining (9, −6) and (2, 1).

Answer: (5.5, −2.5)

  1. x: (9 + 2) ÷ 2 = 5.5
  2. y: (−6 + 1) ÷ 2 = −2.5
3.Find the distance between (6, −1) and (0, −9).

Answer: 10

  1. Horizontal change = 6, vertical change = 8
  2. d = √(62 + 82) = √100
  3. = 10
4.Find the midpoint of the segment joining (5, 5) and (−9, 0).

Answer: (−2, 2.5)

  1. x: (5 + (−9)) ÷ 2 = −2
  2. y: (5 + 0) ÷ 2 = 2.5
5.Find the distance between (3, −1) and (0, −5).

Answer: 5

  1. Horizontal change = 3, vertical change = 4
  2. d = √(32 + 42) = √25
  3. = 5
6.Find the distance between (6, 1) and (14, −1), correct to 1 decimal place.

Answer: 8.2

  1. Horizontal change = 8, vertical change = 2
  2. d = √(82 + 22) = √68
  3. = 8.2
7.Find the distance between (5, −1) and (13, −16).

Answer: 17

  1. Horizontal change = 8, vertical change = 15
  2. d = √(82 + 152) = √289
  3. = 17
8.Find the midpoint of the segment joining (−4, −8) and (3, −5).

Answer: (−0.5, −6.5)

  1. x: (−4 + 3) ÷ 2 = −0.5
  2. y: (−8 + (−5)) ÷ 2 = −6.5
9.Find the distance between (−3, 6) and (−8, −6).

Answer: 13

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

Answer: 10

  1. Horizontal change = 6, vertical change = 8
  2. d = √(62 + 82) = √100
  3. = 10
11.Find the midpoint of the segment joining (3, −7) and (−5, −7).

Answer: (−1, −7)

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

Answer: 7.2

  1. Horizontal change = 6, vertical change = 4
  2. d = √(62 + 42) = √52
  3. = 7.2
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