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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 133 · 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 (6, 10) and (16, 18)? (a) (11, 14) (b) (22, 28) (c) (5, 4) (d) (14, 11)
  2. 2.What is the distance between the points (6, 9) and (13, 33)? (a) 31 (b) 26 (c) 25 (d) 625
  3. 3.How far is the point (15, 8) from the origin (0, 0)? (a) 17 (b) 23 (c) 18 (d) 289
  4. 4.What is the midpoint of the line joining (0, 4) and (4, 12)? (a) (2, 4) (b) (8, 2) (c) (2, 8) (d) (4, 16)
  5. 5.What is the midpoint of the line joining (9, 6) and (13, 0)? (a) (11, 3) (b) (3, 11) (c) (22, 6) (d) (2, 3)
  6. 6.What is the distance between the points (9, 0) and (14, 12)? (a) 14 (b) 17 (c) 169 (d) 13
  7. 7.What is the midpoint of the line joining (0, 10) and (2, 2)? (a) (1, 6) (b) (2, 12) (c) (1, 4) (d) (6, 1)
  8. 8.In which quadrant does the point (7, −6) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  9. 9.What is the distance between the points (7, 2) and (15, 8)? (a) 11 (b) 100 (c) 10 (d) 14
  10. 10.What is the distance between the points (0, 8) and (7, 32)? (a) 625 (b) 26 (c) 25 (d) 31
  11. 11.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 25 (c) 5 (d) 6
  12. 12.What is the distance between the points (6, 17) and (18, 1)? (a) 20 (b) 28 (c) 400 (d) 21
  13. 13.In which quadrant does the point (9, −1) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  14. 14.What is the midpoint of the line joining (3, 5) and (5, 3)? (a) (8, 8) (b) (5, 4) (c) (1, 1) (d) (4, 4)
  15. 15.What is the distance between the points (9, 6) and (17, 21)? (a) 18 (b) 23 (c) 17 (d) 289
  16. 16.What is the distance between the points (3, 8) and (7, 11)? (a) 6 (b) 7 (c) 5 (d) 25
  17. 17.What is the midpoint of the line joining (6, 4) and (18, 10)? (a) (6, 3) (b) (7, 12) (c) (24, 14) (d) (12, 7)
  18. 18.What is the distance between the points (7, 3) and (19, 8)? (a) 14 (b) 13 (c) 169 (d) 17
  19. 19.What is the midpoint of the line joining (7, 4) and (15, 2)? (a) (22, 6) (b) (4, 1) (c) (3, 11) (d) (11, 3)
  20. 20.What is the distance between the points (1, 9) and (13, 25)? (a) 400 (b) 20 (c) 28 (d) 21
  21. 21.What is the distance between the points (2, 6) and (8, 14)? (a) 11 (b) 100 (c) 10 (d) 14
  22. 22.What is the distance between the points (1, 21) and (6, 9)? (a) 17 (b) 169 (c) 14 (d) 13
  23. 23.In which quadrant does the point (−4, 5) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  24. 24.What is the distance between the points (6, 0) and (11, 12)? (a) 169 (b) 13 (c) 17 (d) 14
  25. 25.What is the distance between the points (0, 9) and (9, 21)? (a) 225 (b) 16 (c) 15 (d) 21
  26. 26.What is the distance between the points (2, 1) and (8, 9)? (a) 14 (b) 11 (c) 100 (d) 10
  27. 27.What is the distance between the points (7, 4) and (15, 10)? (a) 14 (b) 100 (c) 10 (d) 11
  28. 28.What is the distance between the points (1, 18) and (6, 6)? (a) 17 (b) 14 (c) 13 (d) 169
  29. 29.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 31 (c) 26 (d) 25
  30. 30.In which quadrant does the point (5, −1) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  31. 31.What is the distance between the points (4, 6) and (12, 0)? (a) 10 (b) 11 (c) 100 (d) 14
  32. 32.What is the distance between the points (5, 13) and (14, 1)? (a) 16 (b) 225 (c) 21 (d) 15
  33. 33.What is the midpoint of the line joining (3, 4) and (9, 2)? (a) (3, 1) (b) (6, 3) (c) (3, 6) (d) (12, 6)
  34. 34.What is the distance between the points (8, 17) and (20, 1)? (a) 21 (b) 28 (c) 400 (d) 20
  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 (3, 17) and (12, 5)? (a) 21 (b) 225 (c) 16 (d) 15
  37. 37.In which quadrant does the point (9, 1) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  38. 38.What is the distance between the points (2, 10) and (26, 3)? (a) 25 (b) 26 (c) 625 (d) 31
  39. 39.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 400 (c) 21 (d) 28
  40. 40.What is the midpoint of the line joining (1, 22) and (13, 10)? (a) (16, 7) (b) (7, 16) (c) (6, 6) (d) (14, 32)

Answer key

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

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