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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 250 · 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 (3, 4) and (15, 20)? (a) 20 (b) 21 (c) 400 (d) 28
  2. 2.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 10 (c) 11 (d) 14
  3. 3.What is the midpoint of the line joining (6, 1) and (18, 5)? (a) (3, 12) (b) (6, 2) (c) (24, 6) (d) (12, 3)
  4. 4.How far is the point (7, 24) from the origin (0, 0)? (a) 25 (b) 26 (c) 625 (d) 31
  5. 5.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 16 (c) 225 (d) 15
  6. 6.What is the distance between the points (8, 1) and (12, 4)? (a) 6 (b) 25 (c) 7 (d) 5
  7. 7.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 6 (c) 7 (d) 5
  8. 8.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 13 (c) 169 (d) 17
  9. 9.What is the midpoint of the line joining (4, 0) and (10, 8)? (a) (14, 8) (b) (3, 4) (c) (7, 4) (d) (4, 7)
  10. 10.In which quadrant does the point (−2, −8) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  11. 11.In which quadrant does the point (4, 5) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  12. 12.What is the distance between the points (3, 11) and (6, 7)? (a) 6 (b) 7 (c) 5 (d) 25
  13. 13.What is the distance between the points (4, 24) and (12, 9)? (a) 23 (b) 289 (c) 18 (d) 17
  14. 14.What is the midpoint of the line joining (10, 2) and (20, 10)? (a) (15, 6) (b) (30, 12) (c) (6, 15) (d) (5, 4)
  15. 15.What is the distance between the points (0, 1) and (3, 5)? (a) 7 (b) 25 (c) 6 (d) 5
  16. 16.What is the distance between the points (8, 1) and (20, 6)? (a) 17 (b) 14 (c) 13 (d) 169
  17. 17.What is the midpoint of the line joining (2, 10) and (8, 2)? (a) (10, 12) (b) (5, 6) (c) (6, 5) (d) (3, 4)
  18. 18.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 21 (c) 225 (d) 15
  19. 19.What is the distance between the points (4, 11) and (7, 7)? (a) 6 (b) 5 (c) 25 (d) 7
  20. 20.What is the distance between the points (7, 14) and (16, 2)? (a) 21 (b) 15 (c) 16 (d) 225
  21. 21.In which quadrant does the point (−8, 2) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  22. 22.What is the distance between the points (7, 20) and (15, 5)? (a) 17 (b) 18 (c) 289 (d) 23
  23. 23.In which quadrant does the point (−3, 5) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  24. 24.In which quadrant does the point (2, −5) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  25. 25.What is the distance between the points (1, 10) and (7, 2)? (a) 10 (b) 100 (c) 14 (d) 11
  26. 26.What is the distance between the points (6, 14) and (18, 5)? (a) 225 (b) 15 (c) 16 (d) 21
  27. 27.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 289 (c) 17 (d) 18
  28. 28.What is the midpoint of the line joining (6, 6) and (12, 14)? (a) (3, 4) (b) (9, 10) (c) (10, 9) (d) (18, 20)
  29. 29.What is the midpoint of the line joining (0, 8) and (6, 18)? (a) (3, 13) (b) (3, 5) (c) (13, 3) (d) (6, 26)
  30. 30.In which quadrant does the point (−5, 1) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  31. 31.What is the midpoint of the line joining (4, 8) and (6, 14)? (a) (1, 3) (b) (11, 5) (c) (5, 11) (d) (10, 22)
  32. 32.What is the distance between the points (3, 15) and (11, 0)? (a) 17 (b) 18 (c) 289 (d) 23
  33. 33.What is the distance between the points (3, 4) and (18, 12)? (a) 23 (b) 18 (c) 289 (d) 17
  34. 34.What is the midpoint of the line joining (10, 12) and (20, 4)? (a) (30, 16) (b) (8, 15) (c) (15, 8) (d) (5, 4)
  35. 35.What is the distance between the points (2, 1) and (14, 10)? (a) 21 (b) 225 (c) 16 (d) 15
  36. 36.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 289 (c) 18 (d) 17
  37. 37.What is the distance between the points (2, 3) and (8, 11)? (a) 14 (b) 100 (c) 11 (d) 10
  38. 38.In which quadrant does the point (−7, −8) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  39. 39.In which quadrant does the point (2, −1) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  40. 40.What is the distance between the points (4, 5) and (9, 17)? (a) 13 (b) 17 (c) 14 (d) 169

Answer key

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

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