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9th Grade Coordinates: Quadrants, Midpoints and Distance Worksheet — Level 2 — Answers

Answer sheet with worked solutions for the 9th Grade geometry worksheet.

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9th Grade Coordinates: Quadrants, Midpoints and Distance Worksheet — Level 2 — 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 (9, 4) and (0, 0).

Answer: (4.5, 2)

  1. x: (9 + 0) ÷ 2 = 4.5
  2. y: (4 + 0) ÷ 2 = 2
2.In which quadrant is the point (3, 7)?
  1. Afirst
  2. Bsecond
  3. Cthird
  4. Dfourth

Answer: first

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

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

4.In which quadrant is the point (−4, 3)?
  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 (−7, −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.

6.Find the midpoint of the segment joining (1, −9) and (−8, 5).

Answer: (−3.5, −2)

  1. x: (1 + (−8)) ÷ 2 = −3.5
  2. y: (−9 + 5) ÷ 2 = −2
7.Find the midpoint of the segment joining (4, −4) and (5, 9).

Answer: (4.5, 2.5)

  1. x: (4 + 5) ÷ 2 = 4.5
  2. y: (−4 + 9) ÷ 2 = 2.5
8.Find the midpoint of the segment joining (5, −2) and (5, 1).

Answer: (5, −0.5)

  1. x: (5 + 5) ÷ 2 = 5
  2. y: (−2 + 1) ÷ 2 = −0.5
9.In which quadrant is the point (3, 9)?
  1. Afirst
  2. Bsecond
  3. Cthird
  4. Dfourth

Answer: first

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

10.In which quadrant is the point (9, −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.

11.Find the midpoint of the segment joining (−9, 8) and (−1, 5).

Answer: (−5, 6.5)

  1. x: (−9 + (−1)) ÷ 2 = −5
  2. y: (8 + 5) ÷ 2 = 6.5
12.In which quadrant is the point (−7, −5)?
  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.

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