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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 570 · 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 (8, 10) and (12, 7)? (a) 5 (b) 6 (c) 7 (d) 25
  2. 2.What is the distance between the points (1, 11) and (13, 2)? (a) 16 (b) 15 (c) 21 (d) 225
  3. 3.What is the distance between the points (8, 6) and (16, 21)? (a) 23 (b) 17 (c) 18 (d) 289
  4. 4.What is the midpoint of the line joining (7, 5) and (11, 13)? (a) (18, 18) (b) (10, 9) (c) (2, 4) (d) (9, 9)
  5. 5.What is the midpoint of the line joining (6, 14) and (12, 10)? (a) (18, 24) (b) (12, 9) (c) (9, 12) (d) (3, 2)
  6. 6.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 625 (c) 25 (d) 26
  7. 7.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 5 (c) 25 (d) 6
  8. 8.What is the distance between the points (4, 4) and (16, 13)? (a) 225 (b) 15 (c) 21 (d) 16
  9. 9.What is the midpoint of the line joining (1, 9) and (5, 1)? (a) (6, 10) (b) (3, 5) (c) (2, 4) (d) (5, 3)
  10. 10.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 18 (c) 17 (d) 23
  11. 11.What is the midpoint of the line joining (7, 22) and (9, 10)? (a) (16, 32) (b) (16, 8) (c) (1, 6) (d) (8, 16)
  12. 12.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 26 (c) 25 (d) 31
  13. 13.In which quadrant does the point (2, −9) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  14. 14.What is the distance between the points (9, 11) and (21, 2)? (a) 15 (b) 21 (c) 225 (d) 16
  15. 15.What is the midpoint of the line joining (1, 7) and (9, 1)? (a) (5, 4) (b) (4, 3) (c) (10, 8) (d) (4, 5)
  16. 16.What is the distance between the points (8, 0) and (11, 4)? (a) 5 (b) 7 (c) 6 (d) 25
  17. 17.What is the midpoint of the line joining (4, 2) and (6, 10)? (a) (5, 6) (b) (1, 4) (c) (6, 5) (d) (10, 12)
  18. 18.What is the midpoint of the line joining (6, 11) and (8, 3)? (a) (8, 7) (b) (1, 4) (c) (7, 7) (d) (14, 14)
  19. 19.What is the midpoint of the line joining (10, 14) and (22, 2)? (a) (8, 16) (b) (16, 8) (c) (32, 16) (d) (6, 6)
  20. 20.In which quadrant does the point (2, −2) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  21. 21.In which quadrant does the point (−1, 9) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  22. 22.In which quadrant does the point (2, 5) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  23. 23.What is the distance between the points (5, 1) and (17, 6)? (a) 14 (b) 17 (c) 13 (d) 169
  24. 24.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 14 (c) 11 (d) 100
  25. 25.In which quadrant does the point (−9, −3) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  26. 26.What is the midpoint of the line joining (8, 9) and (20, 15)? (a) (12, 14) (b) (14, 12) (c) (28, 24) (d) (6, 3)
  27. 27.What is the distance between the points (8, 1) and (11, 5)? (a) 25 (b) 7 (c) 6 (d) 5
  28. 28.What is the midpoint of the line joining (8, 5) and (10, 9)? (a) (1, 2) (b) (9, 7) (c) (7, 9) (d) (18, 14)
  29. 29.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 28 (c) 20 (d) 400
  30. 30.What is the distance between the points (5, 6) and (17, 11)? (a) 14 (b) 17 (c) 13 (d) 169
  31. 31.What is the distance between the points (4, 5) and (9, 17)? (a) 17 (b) 14 (c) 169 (d) 13
  32. 32.What is the midpoint of the line joining (3, 12) and (11, 10)? (a) (4, 1) (b) (11, 7) (c) (7, 11) (d) (14, 22)
  33. 33.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 28 (c) 20 (d) 400
  34. 34.What is the midpoint of the line joining (0, 7) and (10, 11)? (a) (5, 2) (b) (9, 5) (c) (5, 9) (d) (10, 18)
  35. 35.In which quadrant does the point (6, 6) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  36. 36.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 7 (c) 6 (d) 5
  37. 37.What is the midpoint of the line joining (2, 10) and (14, 6)? (a) (9, 8) (b) (16, 16) (c) (8, 8) (d) (6, 2)
  38. 38.What is the midpoint of the line joining (1, 18) and (3, 8)? (a) (13, 2) (b) (1, 5) (c) (4, 26) (d) (2, 13)
  39. 39.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 225 (c) 21 (d) 15
  40. 40.What is the distance between the points (7, 14) and (22, 6)? (a) 18 (b) 23 (c) 17 (d) 289

Answer key

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

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