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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 984 · 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.In which quadrant does the point (9, 2) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  2. 2.What is the distance between the points (5, 5) and (13, 20)? (a) 23 (b) 18 (c) 289 (d) 17
  3. 3.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 21 (c) 15 (d) 225
  4. 4.What is the distance between the points (6, 10) and (18, 5)? (a) 17 (b) 13 (c) 169 (d) 14
  5. 5.In which quadrant does the point (−4, 2) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  6. 6.What is the midpoint of the line joining (5, 10) and (7, 20)? (a) (6, 15) (b) (1, 5) (c) (12, 30) (d) (15, 6)
  7. 7.What is the distance between the points (1, 12) and (10, 0)? (a) 225 (b) 16 (c) 15 (d) 21
  8. 8.What is the midpoint of the line joining (6, 3) and (18, 13)? (a) (8, 12) (b) (6, 5) (c) (24, 16) (d) (12, 8)
  9. 9.In which quadrant does the point (2, 9) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  10. 10.What is the distance between the points (2, 4) and (6, 1)? (a) 5 (b) 6 (c) 25 (d) 7
  11. 11.What is the midpoint of the line joining (0, 17) and (12, 9)? (a) (13, 6) (b) (6, 13) (c) (12, 26) (d) (6, 4)
  12. 12.What is the distance between the points (4, 2) and (19, 10)? (a) 18 (b) 23 (c) 17 (d) 289
  13. 13.What is the midpoint of the line joining (5, 4) and (17, 10)? (a) (6, 3) (b) (7, 11) (c) (11, 7) (d) (22, 14)
  14. 14.In which quadrant does the point (2, 1) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  15. 15.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 14 (c) 10 (d) 11
  16. 16.What is the distance between the points (8, 9) and (20, 4)? (a) 169 (b) 17 (c) 14 (d) 13
  17. 17.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 17 (c) 18 (d) 289
  18. 18.In which quadrant does the point (−1, 4) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  19. 19.What is the distance between the points (3, 1) and (7, 4)? (a) 25 (b) 6 (c) 5 (d) 7
  20. 20.What is the midpoint of the line joining (1, 6) and (7, 12)? (a) (8, 18) (b) (9, 4) (c) (4, 9) (d) (3, 3)
  21. 21.In which quadrant does the point (−2, 9) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  22. 22.What is the midpoint of the line joining (0, 11) and (12, 3)? (a) (6, 7) (b) (7, 6) (c) (12, 14) (d) (6, 4)
  23. 23.What is the distance between the points (8, 12) and (20, 7)? (a) 169 (b) 13 (c) 17 (d) 14
  24. 24.In which quadrant does the point (2, −6) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  25. 25.What is the distance between the points (8, 3) and (11, 7)? (a) 5 (b) 25 (c) 6 (d) 7
  26. 26.How far is the point (12, 9) from the origin (0, 0)? (a) 16 (b) 225 (c) 15 (d) 21
  27. 27.What is the midpoint of the line joining (0, 2) and (2, 4)? (a) (2, 6) (b) (3, 1) (c) (1, 1) (d) (1, 3)
  28. 28.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 400 (c) 21 (d) 20
  29. 29.In which quadrant does the point (9, −8) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  30. 30.In which quadrant does the point (−9, −9) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  31. 31.What is the midpoint of the line joining (7, 17) and (13, 7)? (a) (20, 24) (b) (3, 5) (c) (10, 12) (d) (12, 10)
  32. 32.What is the midpoint of the line joining (0, 2) and (12, 4)? (a) (3, 6) (b) (6, 3) (c) (6, 1) (d) (12, 6)
  33. 33.What is the distance between the points (6, 16) and (18, 0)? (a) 400 (b) 20 (c) 21 (d) 28
  34. 34.In which quadrant does the point (1, 4) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  35. 35.What is the midpoint of the line joining (4, 0) and (12, 4)? (a) (4, 2) (b) (16, 4) (c) (2, 8) (d) (8, 2)
  36. 36.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 18 (c) 23 (d) 17
  37. 37.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 11 (c) 14 (d) 10
  38. 38.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 7 (c) 5 (d) 25
  39. 39.What is the distance between the points (1, 9) and (4, 13)? (a) 7 (b) 6 (c) 25 (d) 5
  40. 40.What is the midpoint of the line joining (2, 10) and (8, 20)? (a) (3, 5) (b) (15, 5) (c) (5, 15) (d) (10, 30)

Answer key

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

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