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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 808 · 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 (2, 3) and (10, 9)? (a) 100 (b) 14 (c) 10 (d) 11
  2. 2.What is the distance between the points (3, 33) and (10, 9)? (a) 625 (b) 31 (c) 26 (d) 25
  3. 3.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 16 (c) 225 (d) 15
  4. 4.What is the midpoint of the line joining (4, 7) and (10, 17)? (a) (14, 24) (b) (7, 12) (c) (3, 5) (d) (12, 7)
  5. 5.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 14 (c) 11 (d) 10
  6. 6.What is the distance between the points (5, 18) and (17, 2)? (a) 28 (b) 21 (c) 400 (d) 20
  7. 7.What is the midpoint of the line joining (0, 10) and (6, 6)? (a) (3, 2) (b) (6, 16) (c) (8, 3) (d) (3, 8)
  8. 8.What is the distance between the points (2, 9) and (8, 17)? (a) 100 (b) 11 (c) 14 (d) 10
  9. 9.In which quadrant does the point (2, 5) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  10. 10.What is the midpoint of the line joining (5, 1) and (9, 7)? (a) (2, 3) (b) (14, 8) (c) (4, 7) (d) (7, 4)
  11. 11.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 7 (c) 6 (d) 5
  12. 12.In which quadrant does the point (−4, 1) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  13. 13.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 23 (c) 17 (d) 18
  14. 14.What is the midpoint of the line joining (8, 0) and (20, 6)? (a) (28, 6) (b) (6, 3) (c) (14, 3) (d) (3, 14)
  15. 15.What is the distance between the points (1, 6) and (10, 18)? (a) 225 (b) 16 (c) 15 (d) 21
  16. 16.What is the distance between the points (6, 2) and (9, 6)? (a) 6 (b) 25 (c) 5 (d) 7
  17. 17.What is the distance between the points (9, 2) and (33, 9)? (a) 31 (b) 25 (c) 26 (d) 625
  18. 18.In which quadrant does the point (8, 9) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  19. 19.How far is the point (16, 12) from the origin (0, 0)? (a) 400 (b) 20 (c) 21 (d) 28
  20. 20.What is the distance between the points (9, 8) and (12, 4)? (a) 5 (b) 6 (c) 25 (d) 7
  21. 21.In which quadrant does the point (−4, −6) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  22. 22.What is the distance between the points (2, 8) and (6, 5)? (a) 6 (b) 7 (c) 25 (d) 5
  23. 23.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 10 (c) 11 (d) 100
  24. 24.What is the distance between the points (2, 20) and (11, 8)? (a) 21 (b) 15 (c) 225 (d) 16
  25. 25.What is the distance between the points (9, 0) and (21, 9)? (a) 15 (b) 16 (c) 21 (d) 225
  26. 26.What is the distance between the points (8, 10) and (16, 4)? (a) 11 (b) 100 (c) 10 (d) 14
  27. 27.What is the midpoint of the line joining (1, 0) and (7, 12)? (a) (4, 6) (b) (8, 12) (c) (3, 6) (d) (6, 4)
  28. 28.What is the distance between the points (2, 14) and (10, 8)? (a) 100 (b) 10 (c) 11 (d) 14
  29. 29.In which quadrant does the point (8, 6) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  30. 30.What is the distance between the points (6, 23) and (14, 8)? (a) 18 (b) 289 (c) 23 (d) 17
  31. 31.What is the midpoint of the line joining (5, 11) and (17, 1)? (a) (6, 5) (b) (22, 12) (c) (6, 11) (d) (11, 6)
  32. 32.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 7 (c) 25 (d) 5
  33. 33.What is the distance between the points (6, 2) and (14, 8)? (a) 100 (b) 11 (c) 10 (d) 14
  34. 34.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 23 (c) 289 (d) 17
  35. 35.What is the distance between the points (7, 0) and (10, 4)? (a) 5 (b) 25 (c) 6 (d) 7
  36. 36.What is the distance between the points (8, 1) and (20, 6)? (a) 17 (b) 14 (c) 13 (d) 169
  37. 37.What is the distance between the points (0, 2) and (15, 10)? (a) 17 (b) 289 (c) 23 (d) 18
  38. 38.What is the midpoint of the line joining (9, 8) and (17, 10)? (a) (4, 1) (b) (13, 9) (c) (9, 13) (d) (26, 18)
  39. 39.What is the midpoint of the line joining (5, 2) and (15, 0)? (a) (5, 1) (b) (20, 2) (c) (1, 10) (d) (10, 1)
  40. 40.What is the distance between the points (0, 8) and (12, 13)? (a) 14 (b) 169 (c) 17 (d) 13

Answer key

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

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