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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 219 · 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 (0, 12) and (16, 0)? (a) 21 (b) 28 (c) 400 (d) 20
  2. 2.What is the midpoint of the line joining (7, 4) and (11, 0)? (a) (9, 2) (b) (18, 4) (c) (2, 9) (d) (2, 2)
  3. 3.What is the midpoint of the line joining (6, 2) and (8, 6)? (a) (4, 7) (b) (7, 4) (c) (14, 8) (d) (1, 2)
  4. 4.What is the midpoint of the line joining (5, 16) and (11, 6)? (a) (11, 8) (b) (16, 22) (c) (3, 5) (d) (8, 11)
  5. 5.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 14 (c) 10 (d) 11
  6. 6.What is the distance between the points (7, 8) and (31, 1)? (a) 26 (b) 25 (c) 625 (d) 31
  7. 7.What is the distance between the points (4, 20) and (16, 4)? (a) 400 (b) 20 (c) 21 (d) 28
  8. 8.What is the distance between the points (9, 23) and (21, 7)? (a) 21 (b) 20 (c) 28 (d) 400
  9. 9.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 5 (c) 25 (d) 6
  10. 10.In which quadrant does the point (3, −4) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  11. 11.In which quadrant does the point (−8, −2) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  12. 12.What is the distance between the points (7, 22) and (19, 6)? (a) 21 (b) 20 (c) 400 (d) 28
  13. 13.What is the distance between the points (1, 8) and (13, 24)? (a) 28 (b) 400 (c) 21 (d) 20
  14. 14.What is the distance between the points (5, 5) and (17, 14)? (a) 15 (b) 16 (c) 225 (d) 21
  15. 15.What is the distance between the points (2, 11) and (5, 7)? (a) 5 (b) 7 (c) 6 (d) 25
  16. 16.What is the midpoint of the line joining (6, 3) and (16, 7)? (a) (22, 10) (b) (5, 2) (c) (5, 11) (d) (11, 5)
  17. 17.What is the midpoint of the line joining (3, 19) and (13, 7)? (a) (5, 6) (b) (13, 8) (c) (16, 26) (d) (8, 13)
  18. 18.What is the distance between the points (6, 0) and (10, 3)? (a) 6 (b) 5 (c) 25 (d) 7
  19. 19.What is the midpoint of the line joining (0, 10) and (6, 2)? (a) (6, 3) (b) (6, 12) (c) (3, 6) (d) (3, 4)
  20. 20.What is the midpoint of the line joining (4, 8) and (14, 2)? (a) (18, 10) (b) (5, 3) (c) (5, 9) (d) (9, 5)
  21. 21.What is the midpoint of the line joining (0, 0) and (2, 8)? (a) (2, 8) (b) (4, 1) (c) (1, 4) (d) (2, 4)
  22. 22.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 16 (c) 15 (d) 225
  23. 23.What is the midpoint of the line joining (8, 8) and (18, 2)? (a) (5, 13) (b) (5, 3) (c) (26, 10) (d) (13, 5)
  24. 24.What is the distance between the points (1, 8) and (9, 14)? (a) 100 (b) 11 (c) 10 (d) 14
  25. 25.In which quadrant does the point (4, −2) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  26. 26.In which quadrant does the point (4, 2) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  27. 27.What is the distance between the points (5, 4) and (11, 12)? (a) 10 (b) 11 (c) 14 (d) 100
  28. 28.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 14 (c) 11 (d) 10
  29. 29.In which quadrant does the point (−3, 8) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  30. 30.What is the distance between the points (7, 23) and (15, 8)? (a) 17 (b) 289 (c) 18 (d) 23
  31. 31.What is the midpoint of the line joining (8, 12) and (18, 2)? (a) (5, 5) (b) (26, 14) (c) (7, 13) (d) (13, 7)
  32. 32.What is the midpoint of the line joining (10, 0) and (12, 4)? (a) (22, 4) (b) (11, 2) (c) (1, 2) (d) (2, 11)
  33. 33.In which quadrant does the point (8, 5) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  34. 34.In which quadrant does the point (−4, −3) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  35. 35.What is the distance between the points (2, 5) and (17, 13)? (a) 18 (b) 17 (c) 23 (d) 289
  36. 36.In which quadrant does the point (2, −1) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  37. 37.What is the distance between the points (4, 15) and (9, 3)? (a) 169 (b) 14 (c) 13 (d) 17
  38. 38.What is the distance between the points (6, 0) and (12, 8)? (a) 14 (b) 11 (c) 100 (d) 10
  39. 39.What is the distance between the points (9, 0) and (15, 8)? (a) 100 (b) 14 (c) 11 (d) 10
  40. 40.What is the midpoint of the line joining (9, 0) and (21, 12)? (a) (15, 6) (b) (6, 15) (c) (6, 6) (d) (30, 12)

Answer key

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

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