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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 888 · 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 (7, 6) and (31, 13)? (a) 625 (b) 25 (c) 26 (d) 31
  2. 2.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 21 (c) 400 (d) 20
  3. 3.In which quadrant does the point (8, −4) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  4. 4.In which quadrant does the point (−1, 7) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  5. 5.What is the distance between the points (8, 0) and (14, 8)? (a) 100 (b) 10 (c) 11 (d) 14
  6. 6.What is the midpoint of the line joining (3, 10) and (13, 14)? (a) (16, 24) (b) (5, 2) (c) (12, 8) (d) (8, 12)
  7. 7.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 289 (c) 17 (d) 18
  8. 8.What is the distance between the points (4, 20) and (12, 5)? (a) 289 (b) 18 (c) 23 (d) 17
  9. 9.What is the midpoint of the line joining (4, 13) and (10, 7)? (a) (3, 3) (b) (14, 20) (c) (10, 7) (d) (7, 10)
  10. 10.In which quadrant does the point (3, 8) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  11. 11.In which quadrant does the point (−1, −1) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  12. 12.In which quadrant does the point (8, 1) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  13. 13.What is the distance between the points (3, 14) and (19, 2)? (a) 28 (b) 20 (c) 400 (d) 21
  14. 14.What is the distance between the points (0, 5) and (12, 21)? (a) 400 (b) 21 (c) 20 (d) 28
  15. 15.In which quadrant does the point (−1, 9) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  16. 16.What is the midpoint of the line joining (8, 4) and (16, 16)? (a) (12, 10) (b) (4, 6) (c) (24, 20) (d) (10, 12)
  17. 17.What is the distance between the points (5, 3) and (21, 15)? (a) 20 (b) 28 (c) 400 (d) 21
  18. 18.What is the distance between the points (3, 0) and (8, 12)? (a) 14 (b) 13 (c) 17 (d) 169
  19. 19.What is the distance between the points (8, 8) and (11, 4)? (a) 25 (b) 5 (c) 7 (d) 6
  20. 20.What is the midpoint of the line joining (4, 15) and (8, 5)? (a) (10, 6) (b) (2, 5) (c) (12, 20) (d) (6, 10)
  21. 21.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 7 (c) 5 (d) 6
  22. 22.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 14 (c) 11 (d) 10
  23. 23.What is the midpoint of the line joining (8, 12) and (10, 6)? (a) (9, 9) (b) (10, 9) (c) (18, 18) (d) (1, 3)
  24. 24.In which quadrant does the point (9, 3) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  25. 25.What is the distance between the points (6, 9) and (18, 14)? (a) 14 (b) 17 (c) 13 (d) 169
  26. 26.What is the distance between the points (5, 21) and (10, 9)? (a) 13 (b) 169 (c) 14 (d) 17
  27. 27.What is the midpoint of the line joining (4, 6) and (12, 14)? (a) (4, 4) (b) (16, 20) (c) (10, 8) (d) (8, 10)
  28. 28.How far is the point (24, 7) from the origin (0, 0)? (a) 26 (b) 31 (c) 25 (d) 625
  29. 29.What is the distance between the points (0, 0) and (24, 7)? (a) 31 (b) 625 (c) 26 (d) 25
  30. 30.What is the midpoint of the line joining (9, 12) and (15, 6)? (a) (3, 3) (b) (9, 12) (c) (24, 18) (d) (12, 9)
  31. 31.What is the midpoint of the line joining (4, 5) and (16, 13)? (a) (20, 18) (b) (9, 10) (c) (6, 4) (d) (10, 9)
  32. 32.In which quadrant does the point (−4, 3) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  33. 33.In which quadrant does the point (4, −3) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  34. 34.What is the midpoint of the line joining (1, 8) and (13, 4)? (a) (6, 2) (b) (7, 6) (c) (14, 12) (d) (6, 7)
  35. 35.What is the distance between the points (1, 0) and (6, 12)? (a) 17 (b) 13 (c) 14 (d) 169
  36. 36.What is the distance between the points (7, 4) and (15, 10)? (a) 100 (b) 14 (c) 11 (d) 10
  37. 37.What is the distance between the points (7, 19) and (19, 3)? (a) 21 (b) 20 (c) 400 (d) 28
  38. 38.What is the distance between the points (3, 7) and (7, 10)? (a) 7 (b) 5 (c) 6 (d) 25
  39. 39.What is the midpoint of the line joining (2, 2) and (10, 14)? (a) (12, 16) (b) (8, 6) (c) (4, 6) (d) (6, 8)
  40. 40.In which quadrant does the point (−8, 6) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant

Answer key

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

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