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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 195 · 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 (5, 25) and (17, 9)? (a) 20 (b) 28 (c) 21 (d) 400
  2. 2.What is the midpoint of the line joining (4, 15) and (6, 9)? (a) (5, 12) (b) (12, 5) (c) (10, 24) (d) (1, 3)
  3. 3.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 26 (c) 25 (d) 31
  4. 4.What is the distance between the points (1, 17) and (9, 2)? (a) 23 (b) 18 (c) 289 (d) 17
  5. 5.What is the distance between the points (2, 17) and (17, 9)? (a) 17 (b) 289 (c) 18 (d) 23
  6. 6.In which quadrant does the point (−8, 6) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  7. 7.In which quadrant does the point (5, 1) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  8. 8.How far is the point (24, 7) from the origin (0, 0)? (a) 26 (b) 31 (c) 625 (d) 25
  9. 9.What is the distance between the points (9, 4) and (17, 19)? (a) 18 (b) 17 (c) 23 (d) 289
  10. 10.What is the distance between the points (1, 15) and (7, 7)? (a) 10 (b) 100 (c) 14 (d) 11
  11. 11.What is the distance between the points (8, 6) and (17, 18)? (a) 21 (b) 15 (c) 16 (d) 225
  12. 12.In which quadrant does the point (−2, 4) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  13. 13.What is the midpoint of the line joining (2, 8) and (14, 10)? (a) (9, 8) (b) (16, 18) (c) (6, 1) (d) (8, 9)
  14. 14.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 25 (c) 5 (d) 7
  15. 15.In which quadrant does the point (−8, −4) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  16. 16.How far is the point (9, 12) from the origin (0, 0)? (a) 15 (b) 21 (c) 16 (d) 225
  17. 17.What is the midpoint of the line joining (4, 11) and (8, 7)? (a) (6, 9) (b) (9, 6) (c) (2, 2) (d) (12, 18)
  18. 18.In which quadrant does the point (3, 8) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  19. 19.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 20 (c) 400 (d) 21
  20. 20.In which quadrant does the point (6, −5) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  21. 21.In which quadrant does the point (−6, −9) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  22. 22.What is the midpoint of the line joining (6, 6) and (18, 14)? (a) (6, 4) (b) (24, 20) (c) (12, 10) (d) (10, 12)
  23. 23.What is the distance between the points (1, 5) and (4, 1)? (a) 6 (b) 7 (c) 5 (d) 25
  24. 24.What is the distance between the points (5, 9) and (10, 21)? (a) 17 (b) 169 (c) 14 (d) 13
  25. 25.What is the midpoint of the line joining (8, 6) and (18, 8)? (a) (7, 13) (b) (5, 1) (c) (13, 7) (d) (26, 14)
  26. 26.What is the distance between the points (0, 4) and (9, 16)? (a) 21 (b) 16 (c) 15 (d) 225
  27. 27.What is the distance between the points (0, 17) and (8, 2)? (a) 17 (b) 289 (c) 23 (d) 18
  28. 28.In which quadrant does the point (−1, 3) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  29. 29.In which quadrant does the point (−7, 6) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  30. 30.What is the midpoint of the line joining (10, 8) and (14, 10)? (a) (2, 1) (b) (24, 18) (c) (12, 9) (d) (9, 12)
  31. 31.What is the midpoint of the line joining (3, 10) and (11, 22)? (a) (14, 32) (b) (16, 7) (c) (4, 6) (d) (7, 16)
  32. 32.What is the midpoint of the line joining (9, 8) and (15, 10)? (a) (3, 1) (b) (9, 12) (c) (24, 18) (d) (12, 9)
  33. 33.In which quadrant does the point (2, 4) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  34. 34.What is the midpoint of the line joining (8, 7) and (10, 17)? (a) (12, 9) (b) (9, 12) (c) (18, 24) (d) (1, 5)
  35. 35.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 17 (c) 18 (d) 23
  36. 36.In which quadrant does the point (−8, 9) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  37. 37.In which quadrant does the point (8, 3) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  38. 38.In which quadrant does the point (−8, 3) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  39. 39.In which quadrant does the point (−7, −1) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  40. 40.In which quadrant does the point (7, −4) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant

Answer key

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

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