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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 105 · 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 (8, 6) from the origin (0, 0)? (a) 11 (b) 100 (c) 14 (d) 10
  2. 2.What is the midpoint of the line joining (10, 6) and (18, 0)? (a) (4, 3) (b) (3, 14) (c) (14, 3) (d) (28, 6)
  3. 3.In which quadrant does the point (6, −8) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  4. 4.What is the distance between the points (3, 11) and (15, 2)? (a) 225 (b) 21 (c) 16 (d) 15
  5. 5.In which quadrant does the point (2, 6) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  6. 6.What is the distance between the points (5, 15) and (14, 3)? (a) 16 (b) 15 (c) 21 (d) 225
  7. 7.In which quadrant does the point (−1, 1) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  8. 8.What is the midpoint of the line joining (4, 10) and (14, 6)? (a) (8, 9) (b) (5, 2) (c) (18, 16) (d) (9, 8)
  9. 9.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 16 (c) 21 (d) 15
  10. 10.What is the distance between the points (4, 6) and (16, 22)? (a) 21 (b) 400 (c) 28 (d) 20
  11. 11.What is the distance between the points (4, 4) and (12, 19)? (a) 289 (b) 17 (c) 18 (d) 23
  12. 12.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 17 (c) 14 (d) 13
  13. 13.What is the distance between the points (7, 7) and (10, 11)? (a) 7 (b) 25 (c) 6 (d) 5
  14. 14.In which quadrant does the point (2, −5) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  15. 15.In which quadrant does the point (−2, 1) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  16. 16.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 25 (c) 625 (d) 31
  17. 17.What is the distance between the points (3, 6) and (27, 13)? (a) 26 (b) 625 (c) 31 (d) 25
  18. 18.What is the distance between the points (0, 8) and (15, 16)? (a) 17 (b) 289 (c) 18 (d) 23
  19. 19.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 18 (c) 23 (d) 17
  20. 20.In which quadrant does the point (7, 9) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  21. 21.What is the distance between the points (8, 0) and (20, 16)? (a) 20 (b) 21 (c) 400 (d) 28
  22. 22.In which quadrant does the point (−5, 2) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  23. 23.What is the midpoint of the line joining (4, 10) and (6, 2)? (a) (10, 12) (b) (5, 6) (c) (6, 5) (d) (1, 4)
  24. 24.What is the midpoint of the line joining (2, 16) and (4, 10)? (a) (3, 13) (b) (1, 3) (c) (6, 26) (d) (13, 3)
  25. 25.What is the distance between the points (9, 1) and (21, 17)? (a) 21 (b) 28 (c) 20 (d) 400
  26. 26.What is the distance between the points (0, 11) and (24, 4)? (a) 625 (b) 31 (c) 25 (d) 26
  27. 27.What is the distance between the points (4, 13) and (9, 1)? (a) 14 (b) 169 (c) 13 (d) 17
  28. 28.In which quadrant does the point (8, 4) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  29. 29.In which quadrant does the point (9, −2) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  30. 30.What is the midpoint of the line joining (2, 16) and (12, 10)? (a) (5, 3) (b) (7, 13) (c) (14, 26) (d) (13, 7)
  31. 31.What is the midpoint of the line joining (2, 12) and (4, 2)? (a) (6, 14) (b) (1, 5) (c) (7, 3) (d) (3, 7)
  32. 32.What is the distance between the points (3, 14) and (12, 2)? (a) 21 (b) 16 (c) 225 (d) 15
  33. 33.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 6 (c) 25 (d) 5
  34. 34.In which quadrant does the point (−7, 3) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  35. 35.What is the midpoint of the line joining (3, 14) and (5, 4)? (a) (8, 18) (b) (1, 5) (c) (9, 4) (d) (4, 9)
  36. 36.What is the distance between the points (9, 3) and (17, 9)? (a) 100 (b) 14 (c) 11 (d) 10
  37. 37.In which quadrant does the point (3, −1) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  38. 38.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 6 (c) 25 (d) 5
  39. 39.What is the midpoint of the line joining (10, 11) and (22, 1)? (a) (16, 6) (b) (6, 5) (c) (32, 12) (d) (6, 16)
  40. 40.How far is the point (5, 12) from the origin (0, 0)? (a) 13 (b) 14 (c) 17 (d) 169

Answer key

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

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