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Coordinate Geometry Worksheet for Maths Olympiad

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

Answer key

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

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