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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 188 · 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 (4, 3) from the origin (0, 0)? (a) 25 (b) 6 (c) 7 (d) 5
  2. 2.In which quadrant does the point (9, −6) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  3. 3.What is the distance between the points (1, 15) and (9, 0)? (a) 23 (b) 18 (c) 17 (d) 289
  4. 4.In which quadrant does the point (−6, 8) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  5. 5.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 25 (c) 6 (d) 5
  6. 6.What is the midpoint of the line joining (8, 12) and (18, 8)? (a) (10, 13) (b) (26, 20) (c) (13, 10) (d) (5, 2)
  7. 7.What is the midpoint of the line joining (8, 22) and (20, 10)? (a) (16, 14) (b) (6, 6) (c) (28, 32) (d) (14, 16)
  8. 8.What is the distance between the points (0, 2) and (4, 5)? (a) 6 (b) 5 (c) 25 (d) 7
  9. 9.In which quadrant does the point (−3, −8) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  10. 10.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 14 (c) 11 (d) 10
  11. 11.What is the distance between the points (3, 2) and (8, 14)? (a) 169 (b) 13 (c) 14 (d) 17
  12. 12.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 10 (c) 100 (d) 11
  13. 13.What is the midpoint of the line joining (4, 6) and (16, 12)? (a) (20, 18) (b) (6, 3) (c) (10, 9) (d) (9, 10)
  14. 14.In which quadrant does the point (−8, 6) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  15. 15.What is the distance between the points (6, 3) and (10, 0)? (a) 6 (b) 25 (c) 7 (d) 5
  16. 16.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 169 (c) 17 (d) 13
  17. 17.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 28 (c) 400 (d) 20
  18. 18.What is the midpoint of the line joining (5, 2) and (13, 10)? (a) (18, 12) (b) (4, 4) (c) (6, 9) (d) (9, 6)
  19. 19.In which quadrant does the point (4, 8) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  20. 20.In which quadrant does the point (9, 6) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  21. 21.What is the distance between the points (0, 8) and (15, 0)? (a) 289 (b) 23 (c) 18 (d) 17
  22. 22.What is the distance between the points (2, 6) and (18, 18)? (a) 21 (b) 28 (c) 400 (d) 20
  23. 23.In which quadrant does the point (−9, 5) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  24. 24.In which quadrant does the point (1, −1) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  25. 25.In which quadrant does the point (7, −8) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  26. 26.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 17 (c) 289 (d) 18
  27. 27.What is the midpoint of the line joining (2, 1) and (6, 9)? (a) (5, 4) (b) (2, 4) (c) (8, 10) (d) (4, 5)
  28. 28.What is the midpoint of the line joining (1, 7) and (3, 13)? (a) (2, 10) (b) (1, 3) (c) (10, 2) (d) (4, 20)
  29. 29.In which quadrant does the point (−6, −5) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  30. 30.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 16 (c) 15 (d) 21
  31. 31.What is the midpoint of the line joining (7, 1) and (13, 13)? (a) (3, 6) (b) (7, 10) (c) (20, 14) (d) (10, 7)
  32. 32.What is the distance between the points (2, 6) and (10, 21)? (a) 18 (b) 17 (c) 289 (d) 23
  33. 33.What is the midpoint of the line joining (8, 12) and (20, 2)? (a) (7, 14) (b) (28, 14) (c) (6, 5) (d) (14, 7)
  34. 34.What is the distance between the points (5, 11) and (11, 3)? (a) 11 (b) 100 (c) 14 (d) 10
  35. 35.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 18 (c) 17 (d) 289
  36. 36.What is the distance between the points (0, 3) and (12, 19)? (a) 21 (b) 400 (c) 28 (d) 20
  37. 37.What is the midpoint of the line joining (3, 3) and (7, 5)? (a) (10, 8) (b) (2, 1) (c) (4, 5) (d) (5, 4)
  38. 38.In which quadrant does the point (−7, 8) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  39. 39.What is the distance between the points (4, 5) and (13, 17)? (a) 21 (b) 16 (c) 225 (d) 15
  40. 40.How far is the point (12, 9) from the origin (0, 0)? (a) 15 (b) 16 (c) 225 (d) 21

Answer key

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

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