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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 431 · 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 midpoint of the line joining (9, 0) and (19, 10)? (a) (5, 5) (b) (28, 10) (c) (5, 14) (d) (14, 5)
  2. 2.What is the distance between the points (7, 2) and (15, 17)? (a) 23 (b) 17 (c) 18 (d) 289
  3. 3.What is the distance between the points (9, 7) and (17, 1)? (a) 14 (b) 100 (c) 10 (d) 11
  4. 4.What is the midpoint of the line joining (7, 6) and (17, 12)? (a) (12, 9) (b) (9, 12) (c) (5, 3) (d) (24, 18)
  5. 5.What is the distance between the points (0, 2) and (3, 6)? (a) 7 (b) 6 (c) 5 (d) 25
  6. 6.What is the midpoint of the line joining (4, 9) and (12, 19)? (a) (4, 5) (b) (8, 14) (c) (14, 8) (d) (16, 28)
  7. 7.In which quadrant does the point (−1, 2) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  8. 8.What is the midpoint of the line joining (3, 10) and (9, 6)? (a) (6, 8) (b) (8, 6) (c) (12, 16) (d) (3, 2)
  9. 9.In which quadrant does the point (1, −7) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  10. 10.What is the distance between the points (0, 6) and (8, 0)? (a) 11 (b) 10 (c) 100 (d) 14
  11. 11.What is the midpoint of the line joining (4, 3) and (12, 5)? (a) (4, 1) (b) (8, 4) (c) (16, 8) (d) (4, 8)
  12. 12.What is the distance between the points (0, 2) and (8, 17)? (a) 18 (b) 17 (c) 23 (d) 289
  13. 13.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 225 (c) 15 (d) 21
  14. 14.What is the midpoint of the line joining (8, 8) and (20, 14)? (a) (6, 3) (b) (14, 11) (c) (28, 22) (d) (11, 14)
  15. 15.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 25 (c) 5 (d) 7
  16. 16.What is the distance between the points (8, 9) and (32, 2)? (a) 26 (b) 31 (c) 25 (d) 625
  17. 17.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 31 (c) 625 (d) 25
  18. 18.What is the distance between the points (1, 17) and (13, 8)? (a) 21 (b) 15 (c) 16 (d) 225
  19. 19.What is the midpoint of the line joining (0, 16) and (4, 4)? (a) (2, 10) (b) (10, 2) (c) (4, 20) (d) (2, 6)
  20. 20.How far is the point (15, 8) from the origin (0, 0)? (a) 17 (b) 23 (c) 18 (d) 289
  21. 21.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 7 (c) 25 (d) 5
  22. 22.What is the midpoint of the line joining (6, 8) and (8, 0)? (a) (1, 4) (b) (14, 8) (c) (4, 7) (d) (7, 4)
  23. 23.What is the distance between the points (5, 5) and (13, 11)? (a) 11 (b) 10 (c) 100 (d) 14
  24. 24.In which quadrant does the point (−1, 8) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  25. 25.What is the distance between the points (1, 5) and (13, 14)? (a) 21 (b) 225 (c) 16 (d) 15
  26. 26.In which quadrant does the point (−9, −8) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  27. 27.What is the distance between the points (9, 8) and (21, 3)? (a) 13 (b) 14 (c) 17 (d) 169
  28. 28.What is the distance between the points (1, 20) and (13, 4)? (a) 21 (b) 400 (c) 20 (d) 28
  29. 29.In which quadrant does the point (9, 4) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  30. 30.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 14 (c) 100 (d) 11
  31. 31.What is the midpoint of the line joining (0, 6) and (8, 10)? (a) (4, 2) (b) (8, 4) (c) (8, 16) (d) (4, 8)
  32. 32.What is the midpoint of the line joining (8, 1) and (10, 3)? (a) (2, 9) (b) (18, 4) (c) (9, 2) (d) (1, 1)
  33. 33.What is the distance between the points (2, 19) and (10, 4)? (a) 23 (b) 17 (c) 289 (d) 18
  34. 34.What is the midpoint of the line joining (6, 6) and (10, 12)? (a) (16, 18) (b) (8, 9) (c) (2, 3) (d) (9, 8)
  35. 35.What is the distance between the points (2, 18) and (10, 3)? (a) 17 (b) 23 (c) 289 (d) 18
  36. 36.What is the distance between the points (5, 4) and (12, 28)? (a) 25 (b) 31 (c) 625 (d) 26
  37. 37.What is the midpoint of the line joining (8, 4) and (20, 6)? (a) (6, 1) (b) (28, 10) (c) (14, 5) (d) (5, 14)
  38. 38.What is the midpoint of the line joining (1, 11) and (9, 1)? (a) (4, 5) (b) (5, 6) (c) (10, 12) (d) (6, 5)
  39. 39.What is the distance between the points (1, 17) and (16, 9)? (a) 18 (b) 17 (c) 289 (d) 23
  40. 40.What is the midpoint of the line joining (4, 8) and (14, 10)? (a) (9, 9) (b) (5, 1) (c) (18, 18) (d) (10, 9)

Answer key

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

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