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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 208 · 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 (12, 9) from the origin (0, 0)? (a) 21 (b) 225 (c) 16 (d) 15
  2. 2.What is the distance between the points (6, 7) and (9, 3)? (a) 6 (b) 7 (c) 25 (d) 5
  3. 3.What is the midpoint of the line joining (4, 3) and (12, 9)? (a) (6, 8) (b) (4, 3) (c) (16, 12) (d) (8, 6)
  4. 4.What is the distance between the points (5, 4) and (17, 13)? (a) 15 (b) 16 (c) 225 (d) 21
  5. 5.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 400 (c) 28 (d) 20
  6. 6.What is the distance between the points (0, 10) and (8, 4)? (a) 14 (b) 100 (c) 11 (d) 10
  7. 7.How far is the point (12, 5) from the origin (0, 0)? (a) 13 (b) 14 (c) 17 (d) 169
  8. 8.What is the midpoint of the line joining (5, 2) and (11, 6)? (a) (16, 8) (b) (4, 8) (c) (8, 4) (d) (3, 2)
  9. 9.What is the midpoint of the line joining (10, 13) and (16, 9)? (a) (3, 2) (b) (13, 11) (c) (11, 13) (d) (26, 22)
  10. 10.In which quadrant does the point (−8, 4) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  11. 11.What is the distance between the points (4, 20) and (13, 8)? (a) 225 (b) 16 (c) 15 (d) 21
  12. 12.What is the distance between the points (3, 6) and (12, 18)? (a) 225 (b) 21 (c) 15 (d) 16
  13. 13.In which quadrant does the point (1, −5) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  14. 14.In which quadrant does the point (4, −2) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  15. 15.What is the midpoint of the line joining (0, 4) and (6, 16)? (a) (10, 3) (b) (3, 6) (c) (3, 10) (d) (6, 20)
  16. 16.How far is the point (9, 12) from the origin (0, 0)? (a) 15 (b) 21 (c) 16 (d) 225
  17. 17.How far is the point (16, 12) from the origin (0, 0)? (a) 400 (b) 20 (c) 21 (d) 28
  18. 18.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 11 (c) 14 (d) 100
  19. 19.What is the distance between the points (9, 8) and (17, 23)? (a) 23 (b) 17 (c) 289 (d) 18
  20. 20.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 31 (c) 26 (d) 25
  21. 21.What is the distance between the points (6, 3) and (15, 15)? (a) 15 (b) 16 (c) 225 (d) 21
  22. 22.What is the midpoint of the line joining (2, 7) and (4, 9)? (a) (6, 16) (b) (1, 1) (c) (3, 8) (d) (8, 3)
  23. 23.What is the distance between the points (6, 6) and (11, 18)? (a) 17 (b) 13 (c) 14 (d) 169
  24. 24.In which quadrant does the point (1, −8) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  25. 25.What is the midpoint of the line joining (10, 14) and (14, 6)? (a) (10, 12) (b) (24, 20) (c) (12, 10) (d) (2, 4)
  26. 26.In which quadrant does the point (−1, −2) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  27. 27.What is the midpoint of the line joining (7, 3) and (15, 13)? (a) (11, 8) (b) (8, 11) (c) (22, 16) (d) (4, 5)
  28. 28.What is the distance between the points (7, 6) and (19, 22)? (a) 21 (b) 400 (c) 20 (d) 28
  29. 29.What is the distance between the points (7, 0) and (13, 8)? (a) 14 (b) 11 (c) 10 (d) 100
  30. 30.In which quadrant does the point (−6, 1) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  31. 31.What is the distance between the points (9, 4) and (18, 16)? (a) 16 (b) 21 (c) 15 (d) 225
  32. 32.What is the distance between the points (6, 24) and (18, 8)? (a) 28 (b) 21 (c) 400 (d) 20
  33. 33.What is the distance between the points (1, 6) and (13, 22)? (a) 28 (b) 400 (c) 20 (d) 21
  34. 34.What is the distance between the points (0, 19) and (8, 4)? (a) 18 (b) 23 (c) 17 (d) 289
  35. 35.What is the distance between the points (9, 13) and (21, 8)? (a) 17 (b) 169 (c) 13 (d) 14
  36. 36.What is the distance between the points (6, 23) and (14, 8)? (a) 289 (b) 23 (c) 18 (d) 17
  37. 37.In which quadrant does the point (5, −3) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  38. 38.In which quadrant does the point (1, 6) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  39. 39.What is the midpoint of the line joining (3, 5) and (15, 1)? (a) (6, 2) (b) (3, 9) (c) (18, 6) (d) (9, 3)
  40. 40.In which quadrant does the point (−3, 7) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant

Answer key

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

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