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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 89 · 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.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 13 (c) 17 (d) 14
  2. 2.What is the distance between the points (2, 0) and (10, 6)? (a) 11 (b) 14 (c) 10 (d) 100
  3. 3.What is the distance between the points (2, 3) and (7, 15)? (a) 169 (b) 14 (c) 13 (d) 17
  4. 4.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 10 (c) 100 (d) 14
  5. 5.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 10 (c) 14 (d) 11
  6. 6.What is the midpoint of the line joining (8, 6) and (12, 4)? (a) (2, 1) (b) (10, 5) (c) (5, 10) (d) (20, 10)
  7. 7.What is the midpoint of the line joining (1, 12) and (5, 0)? (a) (3, 6) (b) (2, 6) (c) (6, 12) (d) (6, 3)
  8. 8.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 18 (c) 289 (d) 23
  9. 9.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 18 (c) 17 (d) 289
  10. 10.What is the midpoint of the line joining (3, 10) and (11, 22)? (a) (16, 7) (b) (14, 32) (c) (4, 6) (d) (7, 16)
  11. 11.What is the midpoint of the line joining (10, 13) and (18, 3)? (a) (4, 5) (b) (28, 16) (c) (8, 14) (d) (14, 8)
  12. 12.What is the midpoint of the line joining (3, 8) and (5, 12)? (a) (4, 10) (b) (1, 2) (c) (10, 4) (d) (8, 20)
  13. 13.What is the distance between the points (3, 16) and (8, 4)? (a) 17 (b) 169 (c) 13 (d) 14
  14. 14.What is the distance between the points (5, 6) and (9, 9)? (a) 5 (b) 6 (c) 25 (d) 7
  15. 15.How far is the point (9, 12) from the origin (0, 0)? (a) 15 (b) 225 (c) 16 (d) 21
  16. 16.In which quadrant does the point (−3, −6) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  17. 17.What is the midpoint of the line joining (5, 9) and (17, 13)? (a) (12, 11) (b) (22, 22) (c) (6, 2) (d) (11, 11)
  18. 18.What is the distance between the points (8, 11) and (20, 2)? (a) 16 (b) 15 (c) 21 (d) 225
  19. 19.In which quadrant does the point (−8, 4) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  20. 20.What is the distance between the points (8, 13) and (14, 5)? (a) 100 (b) 14 (c) 10 (d) 11
  21. 21.What is the distance between the points (8, 3) and (24, 15)? (a) 28 (b) 20 (c) 400 (d) 21
  22. 22.What is the distance between the points (6, 12) and (11, 0)? (a) 169 (b) 14 (c) 13 (d) 17
  23. 23.What is the distance between the points (0, 7) and (7, 31)? (a) 25 (b) 31 (c) 625 (d) 26
  24. 24.What is the distance between the points (9, 17) and (18, 5)? (a) 16 (b) 15 (c) 21 (d) 225
  25. 25.What is the distance between the points (7, 14) and (19, 5)? (a) 15 (b) 21 (c) 225 (d) 16
  26. 26.What is the distance between the points (6, 12) and (12, 4)? (a) 14 (b) 10 (c) 11 (d) 100
  27. 27.What is the distance between the points (9, 21) and (14, 9)? (a) 169 (b) 17 (c) 13 (d) 14
  28. 28.In which quadrant does the point (3, 3) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  29. 29.What is the distance between the points (3, 3) and (27, 10)? (a) 26 (b) 31 (c) 625 (d) 25
  30. 30.How far is the point (16, 12) from the origin (0, 0)? (a) 400 (b) 21 (c) 20 (d) 28
  31. 31.In which quadrant does the point (9, −7) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  32. 32.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 21 (c) 400 (d) 20
  33. 33.What is the distance between the points (2, 14) and (8, 6)? (a) 100 (b) 11 (c) 14 (d) 10
  34. 34.What is the midpoint of the line joining (9, 1) and (21, 11)? (a) (6, 5) (b) (6, 15) (c) (15, 6) (d) (30, 12)
  35. 35.In which quadrant does the point (−5, −6) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  36. 36.What is the midpoint of the line joining (0, 6) and (12, 8)? (a) (12, 14) (b) (6, 7) (c) (6, 1) (d) (7, 6)
  37. 37.What is the distance between the points (1, 4) and (17, 16)? (a) 21 (b) 28 (c) 400 (d) 20
  38. 38.What is the midpoint of the line joining (4, 6) and (10, 10)? (a) (8, 7) (b) (7, 8) (c) (14, 16) (d) (3, 2)
  39. 39.What is the midpoint of the line joining (6, 9) and (16, 13)? (a) (11, 11) (b) (12, 11) (c) (22, 22) (d) (5, 2)
  40. 40.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 13 (c) 169 (d) 17

Answer key

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

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