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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 596 · 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.What is the midpoint of the line joining (5, 9) and (11, 1)? (a) (5, 8) (b) (3, 4) (c) (8, 5) (d) (16, 10)
  2. 2.What is the midpoint of the line joining (10, 7) and (16, 9)? (a) (26, 16) (b) (3, 1) (c) (8, 13) (d) (13, 8)
  3. 3.In which quadrant does the point (−4, −4) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  4. 4.What is the distance between the points (2, 9) and (10, 3)? (a) 14 (b) 10 (c) 100 (d) 11
  5. 5.What is the midpoint of the line joining (6, 13) and (10, 5)? (a) (2, 4) (b) (8, 9) (c) (16, 18) (d) (9, 8)
  6. 6.What is the distance between the points (3, 5) and (15, 10)? (a) 14 (b) 169 (c) 17 (d) 13
  7. 7.What is the distance between the points (6, 8) and (18, 24)? (a) 28 (b) 400 (c) 20 (d) 21
  8. 8.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 400 (c) 20 (d) 21
  9. 9.What is the midpoint of the line joining (9, 12) and (13, 4)? (a) (8, 11) (b) (2, 4) (c) (11, 8) (d) (22, 16)
  10. 10.What is the midpoint of the line joining (4, 8) and (14, 6)? (a) (5, 1) (b) (9, 7) (c) (18, 14) (d) (7, 9)
  11. 11.What is the distance between the points (5, 17) and (20, 9)? (a) 17 (b) 23 (c) 18 (d) 289
  12. 12.In which quadrant does the point (2, −9) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  13. 13.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 23 (c) 18 (d) 17
  14. 14.What is the midpoint of the line joining (9, 8) and (11, 4)? (a) (20, 12) (b) (1, 2) (c) (10, 6) (d) (6, 10)
  15. 15.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 289 (c) 18 (d) 17
  16. 16.In which quadrant does the point (−8, 2) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  17. 17.What is the distance between the points (2, 0) and (14, 9)? (a) 16 (b) 15 (c) 225 (d) 21
  18. 18.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 14 (c) 10 (d) 11
  19. 19.How far is the point (9, 12) from the origin (0, 0)? (a) 15 (b) 225 (c) 21 (d) 16
  20. 20.What is the distance between the points (6, 20) and (11, 8)? (a) 13 (b) 17 (c) 14 (d) 169
  21. 21.What is the midpoint of the line joining (3, 13) and (13, 3)? (a) (16, 16) (b) (5, 5) (c) (9, 8) (d) (8, 8)
  22. 22.What is the midpoint of the line joining (8, 1) and (12, 3)? (a) (10, 2) (b) (20, 4) (c) (2, 10) (d) (2, 1)
  23. 23.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 13 (c) 17 (d) 169
  24. 24.What is the distance between the points (2, 14) and (7, 2)? (a) 169 (b) 17 (c) 14 (d) 13
  25. 25.In which quadrant does the point (−3, 1) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  26. 26.What is the midpoint of the line joining (1, 12) and (3, 8)? (a) (10, 2) (b) (4, 20) (c) (2, 10) (d) (1, 2)
  27. 27.What is the distance between the points (0, 16) and (6, 8)? (a) 10 (b) 14 (c) 100 (d) 11
  28. 28.In which quadrant does the point (9, 5) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  29. 29.What is the distance between the points (4, 9) and (19, 17)? (a) 18 (b) 289 (c) 23 (d) 17
  30. 30.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 25 (c) 26 (d) 625
  31. 31.In which quadrant does the point (6, 2) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  32. 32.What is the distance between the points (0, 4) and (12, 9)? (a) 14 (b) 17 (c) 169 (d) 13
  33. 33.What is the midpoint of the line joining (9, 5) and (11, 7)? (a) (20, 12) (b) (1, 1) (c) (10, 6) (d) (6, 10)
  34. 34.What is the distance between the points (2, 16) and (10, 1)? (a) 17 (b) 18 (c) 23 (d) 289
  35. 35.What is the midpoint of the line joining (9, 9) and (21, 7)? (a) (8, 15) (b) (6, 1) (c) (15, 8) (d) (30, 16)
  36. 36.In which quadrant does the point (2, −7) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  37. 37.What is the distance between the points (4, 15) and (28, 8)? (a) 26 (b) 31 (c) 25 (d) 625
  38. 38.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 16 (c) 225 (d) 15
  39. 39.What is the distance between the points (2, 9) and (9, 33)? (a) 31 (b) 26 (c) 25 (d) 625
  40. 40.What is the midpoint of the line joining (7, 4) and (9, 8)? (a) (1, 2) (b) (16, 12) (c) (8, 6) (d) (6, 8)

Answer key

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

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