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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 551 · 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, 11) and (18, 6)? (a) 14 (b) 169 (c) 13 (d) 17
  2. 2.In which quadrant does the point (−1, 8) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  3. 3.What is the distance between the points (8, 2) and (16, 8)? (a) 14 (b) 11 (c) 100 (d) 10
  4. 4.In which quadrant does the point (−1, 1) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  5. 5.What is the midpoint of the line joining (5, 6) and (9, 10)? (a) (2, 2) (b) (7, 8) (c) (8, 7) (d) (14, 16)
  6. 6.What is the distance between the points (0, 6) and (9, 18)? (a) 21 (b) 16 (c) 15 (d) 225
  7. 7.What is the midpoint of the line joining (3, 16) and (11, 6)? (a) (14, 22) (b) (7, 11) (c) (11, 7) (d) (4, 5)
  8. 8.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 289 (c) 23 (d) 18
  9. 9.What is the distance between the points (5, 9) and (29, 2)? (a) 625 (b) 25 (c) 31 (d) 26
  10. 10.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 26 (c) 625 (d) 25
  11. 11.What is the midpoint of the line joining (5, 0) and (15, 12)? (a) (20, 12) (b) (10, 6) (c) (6, 10) (d) (5, 6)
  12. 12.What is the distance between the points (2, 14) and (10, 8)? (a) 11 (b) 10 (c) 14 (d) 100
  13. 13.What is the distance between the points (8, 6) and (20, 11)? (a) 13 (b) 17 (c) 169 (d) 14
  14. 14.What is the distance between the points (2, 2) and (5, 6)? (a) 25 (b) 7 (c) 6 (d) 5
  15. 15.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 400 (c) 21 (d) 20
  16. 16.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 10 (c) 14 (d) 11
  17. 17.What is the distance between the points (3, 9) and (9, 17)? (a) 11 (b) 100 (c) 14 (d) 10
  18. 18.What is the distance between the points (2, 14) and (17, 6)? (a) 289 (b) 17 (c) 18 (d) 23
  19. 19.In which quadrant does the point (−3, −1) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  20. 20.What is the midpoint of the line joining (10, 3) and (16, 5)? (a) (4, 13) (b) (3, 1) (c) (26, 8) (d) (13, 4)
  21. 21.What is the distance between the points (2, 4) and (9, 28)? (a) 625 (b) 25 (c) 31 (d) 26
  22. 22.What is the midpoint of the line joining (9, 9) and (15, 5)? (a) (24, 14) (b) (7, 12) (c) (3, 2) (d) (12, 7)
  23. 23.What is the distance between the points (3, 2) and (6, 6)? (a) 6 (b) 7 (c) 25 (d) 5
  24. 24.What is the distance between the points (5, 24) and (12, 0)? (a) 31 (b) 26 (c) 625 (d) 25
  25. 25.What is the midpoint of the line joining (7, 0) and (17, 10)? (a) (5, 12) (b) (5, 5) (c) (24, 10) (d) (12, 5)
  26. 26.What is the distance between the points (9, 15) and (33, 8)? (a) 31 (b) 25 (c) 625 (d) 26
  27. 27.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 28 (c) 20 (d) 21
  28. 28.What is the midpoint of the line joining (3, 10) and (5, 12)? (a) (8, 22) (b) (4, 11) (c) (1, 1) (d) (11, 4)
  29. 29.In which quadrant does the point (−2, 7) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  30. 30.What is the distance between the points (8, 19) and (24, 7)? (a) 28 (b) 400 (c) 21 (d) 20
  31. 31.What is the distance between the points (8, 8) and (11, 12)? (a) 25 (b) 6 (c) 5 (d) 7
  32. 32.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 31 (c) 625 (d) 25
  33. 33.In which quadrant does the point (2, −6) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  34. 34.What is the midpoint of the line joining (5, 10) and (13, 4)? (a) (18, 14) (b) (4, 3) (c) (7, 9) (d) (9, 7)
  35. 35.In which quadrant does the point (−2, 2) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  36. 36.In which quadrant does the point (6, 9) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  37. 37.In which quadrant does the point (5, 4) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  38. 38.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 13 (c) 169 (d) 14
  39. 39.What is the distance between the points (7, 18) and (23, 6)? (a) 21 (b) 20 (c) 400 (d) 28
  40. 40.What is the midpoint of the line joining (5, 8) and (15, 10)? (a) (9, 10) (b) (10, 9) (c) (5, 1) (d) (20, 18)

Answer key

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

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