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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 355 · 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, 15) from the origin (0, 0)? (a) 23 (b) 17 (c) 18 (d) 289
  2. 2.What is the distance between the points (2, 12) and (10, 6)? (a) 10 (b) 14 (c) 100 (d) 11
  3. 3.In which quadrant does the point (6, −7) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  4. 4.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 14 (c) 17 (d) 13
  5. 5.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 10 (c) 100 (d) 14
  6. 6.In which quadrant does the point (4, −9) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  7. 7.How far is the point (24, 7) from the origin (0, 0)? (a) 26 (b) 31 (c) 25 (d) 625
  8. 8.In which quadrant does the point (−2, 2) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  9. 9.In which quadrant does the point (−3, −6) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  10. 10.What is the distance between the points (6, 9) and (9, 13)? (a) 25 (b) 5 (c) 7 (d) 6
  11. 11.What is the distance between the points (2, 12) and (18, 0)? (a) 21 (b) 400 (c) 20 (d) 28
  12. 12.What is the midpoint of the line joining (6, 6) and (10, 10)? (a) (9, 8) (b) (8, 8) (c) (16, 16) (d) (2, 2)
  13. 13.How far is the point (12, 9) from the origin (0, 0)? (a) 16 (b) 21 (c) 225 (d) 15
  14. 14.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 16 (c) 21 (d) 15
  15. 15.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 21 (c) 20 (d) 400
  16. 16.What is the midpoint of the line joining (5, 16) and (17, 4)? (a) (22, 20) (b) (10, 11) (c) (6, 6) (d) (11, 10)
  17. 17.In which quadrant does the point (−3, 4) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  18. 18.What is the distance between the points (9, 1) and (33, 8)? (a) 25 (b) 26 (c) 31 (d) 625
  19. 19.What is the distance between the points (2, 1) and (9, 25)? (a) 625 (b) 25 (c) 31 (d) 26
  20. 20.What is the distance between the points (7, 8) and (15, 14)? (a) 11 (b) 14 (c) 100 (d) 10
  21. 21.What is the midpoint of the line joining (10, 6) and (12, 10)? (a) (1, 2) (b) (8, 11) (c) (11, 8) (d) (22, 16)
  22. 22.What is the distance between the points (4, 12) and (8, 9)? (a) 5 (b) 25 (c) 7 (d) 6
  23. 23.What is the midpoint of the line joining (1, 13) and (9, 7)? (a) (5, 10) (b) (10, 20) (c) (4, 3) (d) (10, 5)
  24. 24.What is the distance between the points (0, 2) and (7, 26)? (a) 31 (b) 625 (c) 25 (d) 26
  25. 25.What is the distance between the points (3, 0) and (12, 12)? (a) 21 (b) 16 (c) 225 (d) 15
  26. 26.What is the midpoint of the line joining (2, 0) and (10, 12)? (a) (7, 6) (b) (12, 12) (c) (4, 6) (d) (6, 6)
  27. 27.In which quadrant does the point (−8, −2) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  28. 28.In which quadrant does the point (−1, 6) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  29. 29.In which quadrant does the point (−7, 4) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  30. 30.What is the distance between the points (6, 4) and (9, 8)? (a) 7 (b) 25 (c) 5 (d) 6
  31. 31.What is the midpoint of the line joining (1, 0) and (11, 12)? (a) (5, 6) (b) (12, 12) (c) (6, 6) (d) (7, 6)
  32. 32.What is the midpoint of the line joining (8, 9) and (16, 7)? (a) (24, 16) (b) (8, 12) (c) (12, 8) (d) (4, 1)
  33. 33.In which quadrant does the point (−8, 3) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  34. 34.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 6 (c) 25 (d) 5
  35. 35.What is the midpoint of the line joining (6, 18) and (10, 6)? (a) (2, 6) (b) (8, 12) (c) (12, 8) (d) (16, 24)
  36. 36.What is the distance between the points (2, 3) and (7, 15)? (a) 14 (b) 17 (c) 13 (d) 169
  37. 37.What is the midpoint of the line joining (6, 2) and (8, 14)? (a) (7, 8) (b) (8, 7) (c) (14, 16) (d) (1, 6)
  38. 38.What is the distance between the points (8, 3) and (11, 7)? (a) 25 (b) 6 (c) 5 (d) 7
  39. 39.In which quadrant does the point (8, 6) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  40. 40.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 10 (c) 14 (d) 11

Answer key

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

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