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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 52 · 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, 24) and (15, 8)? (a) 28 (b) 21 (c) 400 (d) 20
  2. 2.What is the distance between the points (5, 9) and (17, 18)? (a) 16 (b) 15 (c) 21 (d) 225
  3. 3.In which quadrant does the point (1, −3) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  4. 4.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 7 (c) 25 (d) 6
  5. 5.What is the distance between the points (5, 5) and (9, 2)? (a) 5 (b) 25 (c) 7 (d) 6
  6. 6.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 289 (c) 23 (d) 17
  7. 7.In which quadrant does the point (−3, 1) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  8. 8.What is the distance between the points (4, 17) and (10, 9)? (a) 10 (b) 14 (c) 11 (d) 100
  9. 9.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 21 (c) 400 (d) 20
  10. 10.What is the midpoint of the line joining (2, 8) and (10, 10)? (a) (4, 1) (b) (9, 6) (c) (12, 18) (d) (6, 9)
  11. 11.What is the distance between the points (7, 17) and (15, 2)? (a) 289 (b) 17 (c) 23 (d) 18
  12. 12.What is the midpoint of the line joining (2, 4) and (10, 0)? (a) (6, 2) (b) (12, 4) (c) (2, 6) (d) (4, 2)
  13. 13.What is the distance between the points (2, 33) and (9, 9)? (a) 26 (b) 625 (c) 31 (d) 25
  14. 14.What is the distance between the points (0, 9) and (15, 17)? (a) 23 (b) 289 (c) 18 (d) 17
  15. 15.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 15 (c) 225 (d) 16
  16. 16.What is the distance between the points (5, 6) and (10, 18)? (a) 169 (b) 14 (c) 13 (d) 17
  17. 17.In which quadrant does the point (−1, 1) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  18. 18.What is the midpoint of the line joining (10, 8) and (22, 4)? (a) (32, 12) (b) (6, 2) (c) (16, 6) (d) (6, 16)
  19. 19.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 25 (c) 31 (d) 625
  20. 20.What is the midpoint of the line joining (10, 14) and (14, 2)? (a) (12, 8) (b) (8, 12) (c) (2, 6) (d) (24, 16)
  21. 21.In which quadrant does the point (−1, −3) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  22. 22.What is the midpoint of the line joining (7, 12) and (15, 0)? (a) (22, 12) (b) (11, 6) (c) (4, 6) (d) (6, 11)
  23. 23.In which quadrant does the point (2, 8) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  24. 24.In which quadrant does the point (−1, −1) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  25. 25.What is the midpoint of the line joining (7, 14) and (11, 4)? (a) (9, 9) (b) (10, 9) (c) (18, 18) (d) (2, 5)
  26. 26.What is the midpoint of the line joining (1, 4) and (13, 2)? (a) (14, 6) (b) (6, 1) (c) (7, 3) (d) (3, 7)
  27. 27.What is the distance between the points (0, 8) and (15, 0)? (a) 17 (b) 23 (c) 18 (d) 289
  28. 28.What is the midpoint of the line joining (3, 0) and (7, 10)? (a) (2, 5) (b) (5, 5) (c) (6, 5) (d) (10, 10)
  29. 29.In which quadrant does the point (−6, −9) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  30. 30.What is the distance between the points (1, 19) and (13, 3)? (a) 400 (b) 20 (c) 28 (d) 21
  31. 31.What is the distance between the points (3, 8) and (11, 2)? (a) 11 (b) 14 (c) 100 (d) 10
  32. 32.What is the distance between the points (0, 8) and (12, 17)? (a) 16 (b) 225 (c) 15 (d) 21
  33. 33.What is the midpoint of the line joining (4, 9) and (12, 1)? (a) (8, 5) (b) (16, 10) (c) (5, 8) (d) (4, 4)
  34. 34.How far is the point (12, 5) from the origin (0, 0)? (a) 13 (b) 169 (c) 17 (d) 14
  35. 35.In which quadrant does the point (−3, −7) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  36. 36.In which quadrant does the point (−7, 5) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  37. 37.What is the midpoint of the line joining (8, 1) and (10, 11)? (a) (6, 9) (b) (1, 5) (c) (9, 6) (d) (18, 12)
  38. 38.In which quadrant does the point (1, 3) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  39. 39.What is the distance between the points (6, 3) and (15, 15)? (a) 16 (b) 21 (c) 15 (d) 225
  40. 40.What is the midpoint of the line joining (10, 10) and (20, 2)? (a) (15, 6) (b) (5, 4) (c) (6, 15) (d) (30, 12)

Answer key

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

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