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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 503 · 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 (7, 24) from the origin (0, 0)? (a) 625 (b) 26 (c) 25 (d) 31
  2. 2.What is the midpoint of the line joining (6, 8) and (16, 14)? (a) (11, 11) (b) (5, 3) (c) (12, 11) (d) (22, 22)
  3. 3.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 17 (c) 169 (d) 13
  4. 4.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 15 (c) 16 (d) 21
  5. 5.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 25 (c) 6 (d) 7
  6. 6.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 100 (c) 11 (d) 14
  7. 7.What is the midpoint of the line joining (8, 11) and (12, 7)? (a) (20, 18) (b) (9, 10) (c) (10, 9) (d) (2, 2)
  8. 8.What is the midpoint of the line joining (2, 7) and (8, 13)? (a) (3, 3) (b) (10, 20) (c) (5, 10) (d) (10, 5)
  9. 9.What is the distance between the points (3, 19) and (19, 7)? (a) 20 (b) 28 (c) 400 (d) 21
  10. 10.What is the midpoint of the line joining (7, 14) and (11, 8)? (a) (18, 22) (b) (2, 3) (c) (9, 11) (d) (11, 9)
  11. 11.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 25 (c) 5 (d) 6
  12. 12.In which quadrant does the point (−2, −1) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  13. 13.What is the distance between the points (2, 6) and (9, 30)? (a) 625 (b) 26 (c) 31 (d) 25
  14. 14.What is the distance between the points (6, 8) and (12, 16)? (a) 10 (b) 14 (c) 100 (d) 11
  15. 15.In which quadrant does the point (7, −2) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  16. 16.What is the midpoint of the line joining (8, 3) and (12, 5)? (a) (10, 4) (b) (2, 1) (c) (4, 10) (d) (20, 8)
  17. 17.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 21 (c) 15 (d) 16
  18. 18.What is the midpoint of the line joining (3, 17) and (15, 5)? (a) (9, 11) (b) (18, 22) (c) (11, 9) (d) (6, 6)
  19. 19.What is the distance between the points (0, 2) and (9, 14)? (a) 21 (b) 16 (c) 225 (d) 15
  20. 20.What is the distance between the points (6, 30) and (13, 6)? (a) 25 (b) 26 (c) 625 (d) 31
  21. 21.What is the midpoint of the line joining (8, 14) and (14, 10)? (a) (22, 24) (b) (12, 11) (c) (11, 12) (d) (3, 2)
  22. 22.What is the midpoint of the line joining (8, 2) and (16, 6)? (a) (12, 4) (b) (24, 8) (c) (4, 2) (d) (4, 12)
  23. 23.What is the distance between the points (7, 11) and (11, 8)? (a) 25 (b) 5 (c) 7 (d) 6
  24. 24.In which quadrant does the point (8, −4) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  25. 25.What is the midpoint of the line joining (0, 7) and (12, 13)? (a) (6, 10) (b) (12, 20) (c) (10, 6) (d) (6, 3)
  26. 26.What is the midpoint of the line joining (3, 13) and (7, 3)? (a) (2, 5) (b) (10, 16) (c) (8, 5) (d) (5, 8)
  27. 27.How far is the point (24, 7) from the origin (0, 0)? (a) 25 (b) 625 (c) 31 (d) 26
  28. 28.In which quadrant does the point (−1, 8) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  29. 29.What is the distance between the points (4, 13) and (9, 1)? (a) 13 (b) 14 (c) 17 (d) 169
  30. 30.In which quadrant does the point (2, 2) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  31. 31.What is the midpoint of the line joining (4, 8) and (14, 6)? (a) (5, 1) (b) (7, 9) (c) (9, 7) (d) (18, 14)
  32. 32.What is the midpoint of the line joining (0, 8) and (12, 4)? (a) (6, 2) (b) (12, 12) (c) (7, 6) (d) (6, 6)
  33. 33.What is the midpoint of the line joining (1, 5) and (7, 7)? (a) (4, 6) (b) (3, 1) (c) (8, 12) (d) (6, 4)
  34. 34.What is the distance between the points (8, 8) and (16, 2)? (a) 10 (b) 14 (c) 100 (d) 11
  35. 35.What is the distance between the points (6, 3) and (10, 0)? (a) 5 (b) 6 (c) 25 (d) 7
  36. 36.What is the distance between the points (3, 19) and (8, 7)? (a) 17 (b) 169 (c) 14 (d) 13
  37. 37.What is the distance between the points (8, 15) and (14, 7)? (a) 14 (b) 11 (c) 100 (d) 10
  38. 38.What is the midpoint of the line joining (1, 1) and (7, 7)? (a) (8, 8) (b) (4, 4) (c) (3, 3) (d) (5, 4)
  39. 39.In which quadrant does the point (6, −3) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  40. 40.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 18 (c) 17 (d) 289

Answer key

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

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