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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 757 · 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 (12, 16) from the origin (0, 0)? (a) 28 (b) 20 (c) 400 (d) 21
  2. 2.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 100 (c) 11 (d) 14
  3. 3.What is the distance between the points (2, 1) and (10, 7)? (a) 14 (b) 100 (c) 11 (d) 10
  4. 4.What is the distance between the points (1, 4) and (13, 20)? (a) 28 (b) 21 (c) 400 (d) 20
  5. 5.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 17 (c) 13 (d) 14
  6. 6.What is the midpoint of the line joining (7, 4) and (13, 0)? (a) (20, 4) (b) (3, 2) (c) (2, 10) (d) (10, 2)
  7. 7.What is the distance between the points (6, 18) and (11, 6)? (a) 17 (b) 14 (c) 169 (d) 13
  8. 8.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 25 (c) 6 (d) 5
  9. 9.What is the midpoint of the line joining (0, 7) and (4, 19)? (a) (2, 6) (b) (2, 13) (c) (4, 26) (d) (13, 2)
  10. 10.In which quadrant does the point (−9, 6) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  11. 11.In which quadrant does the point (9, −2) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  12. 12.What is the distance between the points (3, 6) and (11, 21)? (a) 289 (b) 17 (c) 18 (d) 23
  13. 13.What is the distance between the points (6, 12) and (15, 0)? (a) 225 (b) 15 (c) 16 (d) 21
  14. 14.What is the distance between the points (5, 3) and (20, 11)? (a) 289 (b) 23 (c) 17 (d) 18
  15. 15.What is the distance between the points (9, 9) and (12, 13)? (a) 6 (b) 7 (c) 5 (d) 25
  16. 16.What is the midpoint of the line joining (3, 10) and (15, 0)? (a) (9, 5) (b) (18, 10) (c) (5, 9) (d) (6, 5)
  17. 17.In which quadrant does the point (1, −2) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  18. 18.In which quadrant does the point (8, −5) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  19. 19.What is the distance between the points (1, 4) and (16, 12)? (a) 23 (b) 289 (c) 18 (d) 17
  20. 20.What is the distance between the points (7, 22) and (15, 7)? (a) 23 (b) 17 (c) 289 (d) 18
  21. 21.What is the midpoint of the line joining (1, 5) and (5, 3)? (a) (4, 3) (b) (2, 1) (c) (3, 4) (d) (6, 8)
  22. 22.What is the distance between the points (6, 12) and (10, 9)? (a) 25 (b) 6 (c) 5 (d) 7
  23. 23.What is the distance between the points (0, 9) and (24, 16)? (a) 625 (b) 31 (c) 25 (d) 26
  24. 24.What is the distance between the points (6, 5) and (9, 9)? (a) 25 (b) 7 (c) 6 (d) 5
  25. 25.In which quadrant does the point (−2, 5) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  26. 26.In which quadrant does the point (−3, 1) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  27. 27.What is the distance between the points (3, 7) and (11, 22)? (a) 23 (b) 289 (c) 18 (d) 17
  28. 28.In which quadrant does the point (−7, −4) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  29. 29.In which quadrant does the point (7, 4) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  30. 30.In which quadrant does the point (7, 8) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  31. 31.What is the distance between the points (7, 7) and (15, 13)? (a) 10 (b) 100 (c) 11 (d) 14
  32. 32.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 16 (c) 15 (d) 225
  33. 33.In which quadrant does the point (6, −7) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  34. 34.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 5 (c) 6 (d) 25
  35. 35.What is the distance between the points (4, 9) and (7, 13)? (a) 7 (b) 25 (c) 5 (d) 6
  36. 36.In which quadrant does the point (−8, 6) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  37. 37.What is the midpoint of the line joining (8, 6) and (12, 8)? (a) (2, 1) (b) (7, 10) (c) (20, 14) (d) (10, 7)
  38. 38.In which quadrant does the point (−3, −3) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  39. 39.What is the distance between the points (0, 1) and (16, 13)? (a) 28 (b) 21 (c) 400 (d) 20
  40. 40.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 14 (c) 169 (d) 13

Answer key

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

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