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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 927 · 40 questions
TalentJR

How to solve it (Across, up, Pythagoras): Distance: across = difference of the x values, up = difference of the y values; distance = √(across² + up²). Midpoint = ((x₁ + x₂) ÷ 2, (y₁ + y₂) ÷ 2). Quadrants by signs: (+, +) first, (−, +) second, (−, −) third, (+, −) fourth.

NameDateTime takenScore ___ / 40
  1. 1.In which quadrant does the point (−6, 2) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  2. 2.In which quadrant does the point (−9, −5) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  3. 3.What is the midpoint of the line joining (0, 13) and (2, 7)? (a) (1, 3) (b) (2, 20) (c) (10, 1) (d) (1, 10)
  4. 4.What is the distance between the points (6, 7) and (9, 11)? (a) 6 (b) 7 (c) 5 (d) 25
  5. 5.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 31 (c) 25 (d) 625
  6. 6.What is the distance between the points (3, 9) and (9, 17)? (a) 14 (b) 100 (c) 11 (d) 10
  7. 7.In which quadrant does the point (5, −7) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  8. 8.In which quadrant does the point (3, −6) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  9. 9.What is the distance between the points (5, 8) and (10, 20)? (a) 14 (b) 169 (c) 17 (d) 13
  10. 10.What is the midpoint of the line joining (10, 2) and (20, 8)? (a) (30, 10) (b) (5, 3) (c) (5, 15) (d) (15, 5)
  11. 11.What is the midpoint of the line joining (8, 5) and (14, 17)? (a) (11, 11) (b) (3, 6) (c) (22, 22) (d) (12, 11)
  12. 12.What is the distance between the points (5, 17) and (14, 5)? (a) 16 (b) 21 (c) 225 (d) 15
  13. 13.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 5 (c) 25 (d) 7
  14. 14.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 25 (c) 5 (d) 6
  15. 15.What is the distance between the points (3, 17) and (11, 2)? (a) 17 (b) 289 (c) 23 (d) 18
  16. 16.In which quadrant does the point (−2, 5) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  17. 17.In which quadrant does the point (−5, −8) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  18. 18.How far is the point (24, 7) from the origin (0, 0)? (a) 25 (b) 625 (c) 31 (d) 26
  19. 19.What is the distance between the points (2, 9) and (10, 24)? (a) 17 (b) 289 (c) 23 (d) 18
  20. 20.What is the distance between the points (1, 12) and (4, 8)? (a) 25 (b) 7 (c) 6 (d) 5
  21. 21.What is the midpoint of the line joining (4, 9) and (12, 13)? (a) (16, 22) (b) (8, 11) (c) (4, 2) (d) (11, 8)
  22. 22.What is the midpoint of the line joining (9, 12) and (19, 8)? (a) (14, 10) (b) (5, 2) (c) (28, 20) (d) (10, 14)
  23. 23.What is the distance between the points (6, 8) and (21, 0)? (a) 23 (b) 18 (c) 289 (d) 17
  24. 24.What is the midpoint of the line joining (5, 8) and (7, 2)? (a) (5, 6) (b) (6, 5) (c) (12, 10) (d) (1, 3)
  25. 25.What is the distance between the points (2, 18) and (11, 6)? (a) 21 (b) 16 (c) 225 (d) 15
  26. 26.What is the midpoint of the line joining (8, 0) and (20, 10)? (a) (28, 10) (b) (14, 5) (c) (5, 14) (d) (6, 5)
  27. 27.What is the midpoint of the line joining (1, 8) and (5, 2)? (a) (6, 10) (b) (5, 3) (c) (2, 3) (d) (3, 5)
  28. 28.What is the distance between the points (5, 2) and (8, 6)? (a) 6 (b) 5 (c) 7 (d) 25
  29. 29.What is the distance between the points (8, 17) and (14, 9)? (a) 100 (b) 11 (c) 10 (d) 14
  30. 30.In which quadrant does the point (−8, −9) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  31. 31.In which quadrant does the point (6, 3) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  32. 32.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 16 (c) 15 (d) 21
  33. 33.What is the distance between the points (0, 9) and (8, 24)? (a) 23 (b) 289 (c) 18 (d) 17
  34. 34.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 20 (c) 400 (d) 28
  35. 35.In which quadrant does the point (−4, 2) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  36. 36.What is the distance between the points (0, 7) and (4, 10)? (a) 25 (b) 6 (c) 5 (d) 7
  37. 37.What is the distance between the points (4, 4) and (9, 16)? (a) 169 (b) 13 (c) 17 (d) 14
  38. 38.What is the midpoint of the line joining (4, 8) and (10, 6)? (a) (8, 7) (b) (3, 1) (c) (7, 7) (d) (14, 14)
  39. 39.What is the distance between the points (3, 14) and (12, 2)? (a) 21 (b) 16 (c) 15 (d) 225
  40. 40.What is the midpoint of the line joining (3, 15) and (7, 9)? (a) (2, 3) (b) (12, 5) (c) (5, 12) (d) (10, 24)

Answer key

  1. Second quadrant
  2. Third quadrant
  3. (1, 10)
  4. 5
  5. 25
  6. 10
  7. Fourth quadrant
  8. Fourth quadrant
  9. 13
  10. (15, 5)
  11. (11, 11)
  12. 15
  13. 5
  14. 5
  15. 17
  16. Second quadrant
  17. Third quadrant
  18. 25
  19. 17
  20. 5
  21. (8, 11)
  22. (14, 10)
  23. 17
  24. (6, 5)
  25. 15
  26. (14, 5)
  27. (3, 5)
  28. 5
  29. 10
  30. Third quadrant
  31. First quadrant
  32. 15
  33. 17
  34. 20
  35. Second quadrant
  36. 5
  37. 13
  38. (7, 7)
  39. 15
  40. (5, 12)

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