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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 385 · 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 distance between the points (1, 7) and (5, 10)? (a) 25 (b) 5 (c) 6 (d) 7
  2. 2.How far is the point (12, 9) from the origin (0, 0)? (a) 16 (b) 21 (c) 15 (d) 225
  3. 3.What is the midpoint of the line joining (6, 5) and (14, 7)? (a) (6, 10) (b) (20, 12) (c) (10, 6) (d) (4, 1)
  4. 4.What is the midpoint of the line joining (8, 8) and (16, 12)? (a) (10, 12) (b) (4, 2) (c) (24, 20) (d) (12, 10)
  5. 5.What is the midpoint of the line joining (9, 15) and (19, 3)? (a) (5, 6) (b) (14, 9) (c) (28, 18) (d) (9, 14)
  6. 6.In which quadrant does the point (−7, 2) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  7. 7.What is the midpoint of the line joining (6, 2) and (16, 4)? (a) (3, 11) (b) (22, 6) (c) (5, 1) (d) (11, 3)
  8. 8.What is the midpoint of the line joining (4, 6) and (8, 10)? (a) (8, 6) (b) (12, 16) (c) (2, 2) (d) (6, 8)
  9. 9.How far is the point (12, 5) from the origin (0, 0)? (a) 13 (b) 17 (c) 14 (d) 169
  10. 10.What is the distance between the points (0, 5) and (24, 12)? (a) 26 (b) 25 (c) 31 (d) 625
  11. 11.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 289 (c) 23 (d) 17
  12. 12.What is the distance between the points (8, 7) and (20, 16)? (a) 16 (b) 15 (c) 21 (d) 225
  13. 13.In which quadrant does the point (−4, −1) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  14. 14.What is the distance between the points (2, 24) and (10, 9)? (a) 17 (b) 23 (c) 18 (d) 289
  15. 15.What is the distance between the points (4, 3) and (8, 6)? (a) 6 (b) 7 (c) 5 (d) 25
  16. 16.In which quadrant does the point (−4, −4) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  17. 17.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 17 (c) 18 (d) 289
  18. 18.In which quadrant does the point (8, −9) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  19. 19.What is the distance between the points (0, 14) and (16, 2)? (a) 20 (b) 28 (c) 400 (d) 21
  20. 20.What is the distance between the points (2, 16) and (14, 0)? (a) 28 (b) 21 (c) 20 (d) 400
  21. 21.What is the midpoint of the line joining (2, 8) and (4, 16)? (a) (3, 12) (b) (6, 24) (c) (12, 3) (d) (1, 4)
  22. 22.What is the midpoint of the line joining (7, 14) and (9, 10)? (a) (12, 8) (b) (1, 2) (c) (8, 12) (d) (16, 24)
  23. 23.How far is the point (9, 12) from the origin (0, 0)? (a) 15 (b) 21 (c) 225 (d) 16
  24. 24.In which quadrant does the point (4, 5) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  25. 25.In which quadrant does the point (−1, −4) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  26. 26.What is the midpoint of the line joining (3, 10) and (7, 22)? (a) (16, 5) (b) (2, 6) (c) (10, 32) (d) (5, 16)
  27. 27.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 169 (c) 17 (d) 13
  28. 28.What is the distance between the points (0, 2) and (4, 5)? (a) 7 (b) 6 (c) 25 (d) 5
  29. 29.What is the midpoint of the line joining (10, 10) and (14, 6)? (a) (8, 12) (b) (24, 16) (c) (2, 2) (d) (12, 8)
  30. 30.What is the midpoint of the line joining (1, 2) and (13, 10)? (a) (14, 12) (b) (6, 4) (c) (6, 7) (d) (7, 6)
  31. 31.What is the distance between the points (1, 1) and (7, 9)? (a) 14 (b) 100 (c) 11 (d) 10
  32. 32.What is the midpoint of the line joining (1, 8) and (7, 16)? (a) (3, 4) (b) (12, 4) (c) (8, 24) (d) (4, 12)
  33. 33.What is the midpoint of the line joining (6, 8) and (10, 0)? (a) (2, 4) (b) (16, 8) (c) (4, 8) (d) (8, 4)
  34. 34.In which quadrant does the point (−3, 7) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  35. 35.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 25 (c) 5 (d) 6
  36. 36.What is the midpoint of the line joining (6, 5) and (10, 1)? (a) (8, 3) (b) (16, 6) (c) (3, 8) (d) (2, 2)
  37. 37.In which quadrant does the point (−8, 2) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  38. 38.What is the distance between the points (3, 7) and (6, 11)? (a) 25 (b) 5 (c) 6 (d) 7
  39. 39.What is the midpoint of the line joining (9, 1) and (11, 13)? (a) (10, 7) (b) (20, 14) (c) (7, 10) (d) (1, 6)
  40. 40.In which quadrant does the point (−6, 7) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant

Answer key

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

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