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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 554 · 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.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 7 (c) 6 (d) 5
  2. 2.What is the midpoint of the line joining (8, 7) and (10, 3)? (a) (1, 2) (b) (9, 5) (c) (5, 9) (d) (18, 10)
  3. 3.What is the midpoint of the line joining (7, 4) and (9, 8)? (a) (8, 6) (b) (16, 12) (c) (1, 2) (d) (6, 8)
  4. 4.What is the midpoint of the line joining (2, 2) and (14, 8)? (a) (6, 3) (b) (8, 5) (c) (5, 8) (d) (16, 10)
  5. 5.What is the midpoint of the line joining (9, 20) and (19, 8)? (a) (5, 6) (b) (15, 14) (c) (28, 28) (d) (14, 14)
  6. 6.What is the distance between the points (4, 4) and (12, 10)? (a) 100 (b) 14 (c) 10 (d) 11
  7. 7.What is the distance between the points (0, 9) and (12, 4)? (a) 169 (b) 17 (c) 13 (d) 14
  8. 8.What is the midpoint of the line joining (2, 10) and (12, 12)? (a) (11, 7) (b) (7, 11) (c) (14, 22) (d) (5, 1)
  9. 9.What is the distance between the points (7, 25) and (14, 1)? (a) 625 (b) 26 (c) 25 (d) 31
  10. 10.What is the distance between the points (5, 5) and (12, 29)? (a) 31 (b) 625 (c) 26 (d) 25
  11. 11.What is the midpoint of the line joining (5, 8) and (7, 16)? (a) (12, 6) (b) (12, 24) (c) (6, 12) (d) (1, 4)
  12. 12.What is the distance between the points (2, 7) and (17, 15)? (a) 23 (b) 18 (c) 17 (d) 289
  13. 13.What is the midpoint of the line joining (10, 4) and (18, 6)? (a) (28, 10) (b) (14, 5) (c) (5, 14) (d) (4, 1)
  14. 14.What is the midpoint of the line joining (8, 10) and (12, 18)? (a) (20, 28) (b) (14, 10) (c) (10, 14) (d) (2, 4)
  15. 15.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 25 (c) 625 (d) 31
  16. 16.What is the distance between the points (2, 21) and (7, 9)? (a) 169 (b) 14 (c) 13 (d) 17
  17. 17.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 16 (c) 15 (d) 225
  18. 18.What is the distance between the points (3, 9) and (11, 3)? (a) 11 (b) 100 (c) 10 (d) 14
  19. 19.What is the midpoint of the line joining (0, 6) and (2, 10)? (a) (2, 16) (b) (8, 1) (c) (1, 8) (d) (1, 2)
  20. 20.What is the distance between the points (7, 4) and (11, 7)? (a) 25 (b) 5 (c) 6 (d) 7
  21. 21.What is the distance between the points (1, 3) and (5, 0)? (a) 25 (b) 6 (c) 5 (d) 7
  22. 22.What is the distance between the points (7, 6) and (19, 11)? (a) 17 (b) 169 (c) 14 (d) 13
  23. 23.What is the distance between the points (4, 12) and (12, 6)? (a) 14 (b) 11 (c) 10 (d) 100
  24. 24.In which quadrant does the point (6, −9) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  25. 25.How far is the point (15, 8) from the origin (0, 0)? (a) 17 (b) 23 (c) 18 (d) 289
  26. 26.In which quadrant does the point (4, −5) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  27. 27.What is the midpoint of the line joining (7, 14) and (9, 2)? (a) (1, 6) (b) (16, 16) (c) (9, 8) (d) (8, 8)
  28. 28.In which quadrant does the point (5, 6) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  29. 29.What is the distance between the points (1, 15) and (13, 6)? (a) 16 (b) 21 (c) 225 (d) 15
  30. 30.In which quadrant does the point (−9, −1) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  31. 31.What is the distance between the points (5, 22) and (13, 7)? (a) 289 (b) 18 (c) 17 (d) 23
  32. 32.What is the midpoint of the line joining (0, 14) and (10, 8)? (a) (10, 22) (b) (11, 5) (c) (5, 11) (d) (5, 3)
  33. 33.What is the distance between the points (4, 6) and (28, 13)? (a) 31 (b) 25 (c) 625 (d) 26
  34. 34.What is the midpoint of the line joining (7, 0) and (15, 8)? (a) (4, 4) (b) (11, 4) (c) (22, 8) (d) (4, 11)
  35. 35.What is the distance between the points (2, 13) and (14, 4)? (a) 21 (b) 16 (c) 225 (d) 15
  36. 36.What is the distance between the points (5, 9) and (17, 25)? (a) 28 (b) 21 (c) 400 (d) 20
  37. 37.In which quadrant does the point (9, 2) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  38. 38.What is the distance between the points (6, 8) and (12, 0)? (a) 11 (b) 100 (c) 14 (d) 10
  39. 39.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 100 (c) 11 (d) 14
  40. 40.What is the distance between the points (3, 7) and (6, 11)? (a) 7 (b) 6 (c) 5 (d) 25

Answer key

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

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