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Year 9 Coordinates: Quadrants, Midpoints and Distance Worksheet — Level 2 — Practice Set 3 — Answers

Answer sheet with worked solutions for the Year 9 geometry worksheet.

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Year 9 Coordinates: Quadrants, Midpoints and Distance Worksheet — Level 2 — 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 (−7, −2) and (−1, 7).

Answer: (−4, 2.5)

  1. x: (−7 + (−1)) ÷ 2 = −4
  2. y: (−2 + 7) ÷ 2 = 2.5
2.Find the midpoint of the segment joining (0, −4) and (2, −2).

Answer: (1, −3)

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

4.Find the midpoint of the segment joining (−2, 3) and (−8, 7).

Answer: (−5, 5)

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

Answer: (3.5, 8)

  1. x: (1 + 6) ÷ 2 = 3.5
  2. y: (8 + 8) ÷ 2 = 8
6.In which quadrant is the point (6, −6)?
  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.

7.In which quadrant is the point (−2, −9)?
  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 (−1, 6) and (9, −7).

Answer: (4, −0.5)

  1. x: (−1 + 9) ÷ 2 = 4
  2. y: (6 + (−7)) ÷ 2 = −0.5
9.Find the midpoint of the segment joining (−3, −6) and (−1, 5).

Answer: (−2, −0.5)

  1. x: (−3 + (−1)) ÷ 2 = −2
  2. y: (−6 + 5) ÷ 2 = −0.5
10.Find the midpoint of the segment joining (−2, 3) and (−4, 3).

Answer: (−3, 3)

  1. x: (−2 + (−4)) ÷ 2 = −3
  2. y: (3 + 3) ÷ 2 = 3
11.In which quadrant is the point (−5, 9)?
  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.

12.In which quadrant is the point (3, −4)?
  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.

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