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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 357 · 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 (6, 8) and (18, 24)? (a) 400 (b) 20 (c) 21 (d) 28
  2. 2.What is the midpoint of the line joining (3, 8) and (13, 12)? (a) (8, 10) (b) (16, 20) (c) (10, 8) (d) (5, 2)
  3. 3.What is the distance between the points (1, 0) and (17, 12)? (a) 28 (b) 21 (c) 20 (d) 400
  4. 4.What is the midpoint of the line joining (9, 6) and (11, 10)? (a) (1, 2) (b) (10, 8) (c) (20, 16) (d) (8, 10)
  5. 5.What is the midpoint of the line joining (7, 8) and (9, 12)? (a) (10, 8) (b) (8, 10) (c) (1, 2) (d) (16, 20)
  6. 6.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 21 (c) 400 (d) 20
  7. 7.What is the distance between the points (8, 3) and (11, 7)? (a) 25 (b) 6 (c) 7 (d) 5
  8. 8.What is the distance between the points (9, 8) and (13, 11)? (a) 5 (b) 7 (c) 6 (d) 25
  9. 9.In which quadrant does the point (1, 4) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  10. 10.What is the distance between the points (1, 20) and (10, 8)? (a) 16 (b) 21 (c) 225 (d) 15
  11. 11.How far is the point (12, 5) from the origin (0, 0)? (a) 13 (b) 17 (c) 169 (d) 14
  12. 12.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 15 (c) 21 (d) 16
  13. 13.How far is the point (24, 7) from the origin (0, 0)? (a) 26 (b) 31 (c) 625 (d) 25
  14. 14.What is the distance between the points (9, 8) and (17, 14)? (a) 11 (b) 14 (c) 10 (d) 100
  15. 15.What is the distance between the points (9, 7) and (24, 15)? (a) 18 (b) 23 (c) 289 (d) 17
  16. 16.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 15 (c) 16 (d) 225
  17. 17.What is the midpoint of the line joining (2, 21) and (6, 9)? (a) (8, 30) (b) (2, 6) (c) (15, 4) (d) (4, 15)
  18. 18.In which quadrant does the point (7, 5) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  19. 19.How far is the point (7, 24) from the origin (0, 0)? (a) 25 (b) 625 (c) 31 (d) 26
  20. 20.In which quadrant does the point (−7, −1) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  21. 21.What is the midpoint of the line joining (10, 1) and (16, 9)? (a) (26, 10) (b) (3, 4) (c) (5, 13) (d) (13, 5)
  22. 22.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 18 (c) 23 (d) 17
  23. 23.What is the midpoint of the line joining (10, 4) and (22, 8)? (a) (16, 6) (b) (32, 12) (c) (6, 2) (d) (6, 16)
  24. 24.In which quadrant does the point (−2, 2) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  25. 25.In which quadrant does the point (2, −2) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  26. 26.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 7 (c) 25 (d) 5
  27. 27.In which quadrant does the point (6, 6) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  28. 28.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 13 (c) 14 (d) 169
  29. 29.What is the distance between the points (0, 2) and (15, 10)? (a) 289 (b) 17 (c) 23 (d) 18
  30. 30.What is the distance between the points (2, 1) and (14, 6)? (a) 17 (b) 13 (c) 169 (d) 14
  31. 31.In which quadrant does the point (−2, 4) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  32. 32.What is the midpoint of the line joining (10, 7) and (20, 3)? (a) (5, 2) (b) (5, 15) (c) (30, 10) (d) (15, 5)
  33. 33.What is the distance between the points (6, 8) and (30, 1)? (a) 31 (b) 625 (c) 25 (d) 26
  34. 34.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 7 (c) 25 (d) 5
  35. 35.What is the midpoint of the line joining (9, 7) and (15, 3)? (a) (24, 10) (b) (3, 2) (c) (5, 12) (d) (12, 5)
  36. 36.In which quadrant does the point (−4, −7) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  37. 37.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 20 (c) 21 (d) 400
  38. 38.In which quadrant does the point (8, −7) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  39. 39.What is the distance between the points (0, 9) and (15, 17)? (a) 18 (b) 23 (c) 289 (d) 17
  40. 40.What is the midpoint of the line joining (5, 20) and (7, 8)? (a) (12, 28) (b) (14, 6) (c) (1, 6) (d) (6, 14)

Answer key

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

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