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Year 11 Coordinates: Quadrants, Midpoints and Distance Worksheet — Level 2 — Practice Set 4 — Answers

Answer sheet with worked solutions for the Year 11 geometry worksheet.

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Year 11 Coordinates: Quadrants, Midpoints and Distance Worksheet — Level 2 — 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 (−7, −8) and (3, 4).

Answer: (−2, −2)

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

Answer: (−8, 4)

  1. x: (−8 + (−8)) ÷ 2 = −8
  2. y: (5 + 3) ÷ 2 = 4
3.Find the midpoint of the segment joining (9, 0) and (−2, 0).

Answer: (3.5, 0)

  1. x: (9 + (−2)) ÷ 2 = 3.5
  2. y: (0 + 0) ÷ 2 = 0
4.In which quadrant is the point (−2, 4)?
  1. Afirst
  2. Bsecond
  3. Cthird
  4. Dfourth

Answer: second

x is negative and y is positive, so the point is in the second quadrant.

5.In which quadrant is the point (−9, 1)?
  1. Afirst
  2. Bsecond
  3. Cthird
  4. Dfourth

Answer: second

x is negative and y is positive, so the point is in the second quadrant.

6.Find the midpoint of the segment joining (4, 5) and (3, 1).

Answer: (3.5, 3)

  1. x: (4 + 3) ÷ 2 = 3.5
  2. y: (5 + 1) ÷ 2 = 3
7.In which quadrant is the point (−8, −7)?
  1. Afirst
  2. Bsecond
  3. Cthird
  4. Dfourth

Answer: third

x is negative and y is negative, so the point is in the third quadrant.

8.Find the midpoint of the segment joining (5, 0) and (−7, −4).

Answer: (−1, −2)

  1. x: (5 + (−7)) ÷ 2 = −1
  2. y: (0 + (−4)) ÷ 2 = −2
9.In which quadrant is the point (9, −2)?
  1. Afirst
  2. Bsecond
  3. Cthird
  4. Dfourth

Answer: fourth

x is positive and y is negative, so the point is in the fourth quadrant.

10.In which quadrant is the point (−9, 6)?
  1. Afirst
  2. Bsecond
  3. Cthird
  4. Dfourth

Answer: second

x is negative and y is positive, so the point is in the second quadrant.

11.In which quadrant is the point (3, −5)?
  1. Afirst
  2. Bsecond
  3. Cthird
  4. Dfourth

Answer: fourth

x is positive and y is negative, so the point is in the fourth quadrant.

12.Find the midpoint of the segment joining (−1, 7) and (6, −5).

Answer: (2.5, 1)

  1. x: (−1 + 6) ÷ 2 = 2.5
  2. y: (7 + (−5)) ÷ 2 = 1
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