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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 116 · 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 distance between the points (1, 7) and (17, 19)? (a) 20 (b) 28 (c) 400 (d) 21
  2. 2.What is the distance between the points (6, 4) and (18, 9)? (a) 17 (b) 14 (c) 169 (d) 13
  3. 3.In which quadrant does the point (−8, −5) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  4. 4.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 400 (c) 21 (d) 20
  5. 5.In which quadrant does the point (−7, 7) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  6. 6.What is the distance between the points (6, 25) and (18, 9)? (a) 28 (b) 400 (c) 20 (d) 21
  7. 7.What is the distance between the points (8, 14) and (16, 8)? (a) 10 (b) 14 (c) 100 (d) 11
  8. 8.In which quadrant does the point (−4, −8) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  9. 9.What is the distance between the points (0, 4) and (7, 28)? (a) 26 (b) 625 (c) 31 (d) 25
  10. 10.What is the midpoint of the line joining (10, 0) and (18, 2)? (a) (1, 14) (b) (4, 1) (c) (28, 2) (d) (14, 1)
  11. 11.In which quadrant does the point (3, 2) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  12. 12.What is the distance between the points (0, 16) and (6, 8)? (a) 14 (b) 100 (c) 10 (d) 11
  13. 13.What is the distance between the points (2, 24) and (10, 9)? (a) 289 (b) 17 (c) 18 (d) 23
  14. 14.In which quadrant does the point (7, 2) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  15. 15.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 10 (c) 11 (d) 14
  16. 16.What is the distance between the points (7, 14) and (13, 6)? (a) 10 (b) 11 (c) 14 (d) 100
  17. 17.What is the distance between the points (3, 1) and (15, 6)? (a) 17 (b) 13 (c) 14 (d) 169
  18. 18.In which quadrant does the point (1, −3) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  19. 19.In which quadrant does the point (2, −1) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  20. 20.How far is the point (12, 9) from the origin (0, 0)? (a) 15 (b) 21 (c) 225 (d) 16
  21. 21.What is the distance between the points (1, 13) and (13, 4)? (a) 16 (b) 225 (c) 21 (d) 15
  22. 22.What is the distance between the points (6, 8) and (18, 3)? (a) 17 (b) 14 (c) 169 (d) 13
  23. 23.In which quadrant does the point (−7, 3) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  24. 24.What is the midpoint of the line joining (0, 8) and (8, 6)? (a) (4, 1) (b) (8, 14) (c) (7, 4) (d) (4, 7)
  25. 25.What is the midpoint of the line joining (2, 16) and (4, 4)? (a) (10, 3) (b) (1, 6) (c) (3, 10) (d) (6, 20)
  26. 26.What is the midpoint of the line joining (1, 3) and (9, 7)? (a) (10, 10) (b) (5, 5) (c) (4, 2) (d) (6, 5)
  27. 27.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 25 (c) 26 (d) 31
  28. 28.In which quadrant does the point (−6, −3) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  29. 29.What is the distance between the points (4, 17) and (13, 5)? (a) 16 (b) 15 (c) 21 (d) 225
  30. 30.What is the midpoint of the line joining (10, 12) and (22, 0)? (a) (32, 12) (b) (6, 16) (c) (6, 6) (d) (16, 6)
  31. 31.What is the distance between the points (2, 4) and (6, 1)? (a) 5 (b) 7 (c) 6 (d) 25
  32. 32.In which quadrant does the point (1, −8) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  33. 33.In which quadrant does the point (−2, 6) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  34. 34.What is the midpoint of the line joining (1, 19) and (3, 7)? (a) (4, 26) (b) (2, 13) (c) (1, 6) (d) (13, 2)
  35. 35.What is the midpoint of the line joining (2, 1) and (14, 11)? (a) (8, 6) (b) (6, 5) (c) (16, 12) (d) (6, 8)
  36. 36.What is the midpoint of the line joining (1, 5) and (9, 3)? (a) (4, 1) (b) (4, 5) (c) (5, 4) (d) (10, 8)
  37. 37.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 7 (c) 5 (d) 6
  38. 38.How far is the point (15, 8) from the origin (0, 0)? (a) 17 (b) 18 (c) 289 (d) 23
  39. 39.In which quadrant does the point (6, −9) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  40. 40.What is the distance between the points (5, 11) and (17, 6)? (a) 17 (b) 13 (c) 169 (d) 14

Answer key

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

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