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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 374 · 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 (0, 2) and (3, 6)? (a) 7 (b) 6 (c) 25 (d) 5
  2. 2.What is the distance between the points (7, 1) and (11, 4)? (a) 6 (b) 5 (c) 25 (d) 7
  3. 3.What is the midpoint of the line joining (2, 7) and (14, 9)? (a) (6, 1) (b) (9, 8) (c) (16, 16) (d) (8, 8)
  4. 4.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 11 (c) 100 (d) 10
  5. 5.What is the distance between the points (4, 1) and (12, 7)? (a) 14 (b) 100 (c) 11 (d) 10
  6. 6.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 289 (c) 18 (d) 23
  7. 7.What is the midpoint of the line joining (7, 10) and (9, 8)? (a) (16, 18) (b) (8, 9) (c) (9, 8) (d) (1, 1)
  8. 8.What is the distance between the points (3, 6) and (7, 9)? (a) 25 (b) 5 (c) 6 (d) 7
  9. 9.In which quadrant does the point (−4, −6) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  10. 10.What is the distance between the points (8, 2) and (12, 5)? (a) 5 (b) 7 (c) 6 (d) 25
  11. 11.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 26 (c) 625 (d) 25
  12. 12.What is the midpoint of the line joining (6, 2) and (12, 0)? (a) (1, 9) (b) (9, 1) (c) (3, 1) (d) (18, 2)
  13. 13.What is the midpoint of the line joining (7, 7) and (13, 1)? (a) (4, 10) (b) (10, 4) (c) (20, 8) (d) (3, 3)
  14. 14.What is the distance between the points (9, 1) and (24, 9)? (a) 18 (b) 289 (c) 23 (d) 17
  15. 15.In which quadrant does the point (−3, 6) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  16. 16.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 5 (c) 25 (d) 7
  17. 17.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 21 (c) 20 (d) 28
  18. 18.What is the midpoint of the line joining (4, 20) and (10, 10)? (a) (3, 5) (b) (15, 7) (c) (14, 30) (d) (7, 15)
  19. 19.What is the distance between the points (9, 15) and (17, 0)? (a) 18 (b) 23 (c) 17 (d) 289
  20. 20.What is the midpoint of the line joining (6, 4) and (18, 10)? (a) (6, 3) (b) (24, 14) (c) (7, 12) (d) (12, 7)
  21. 21.What is the distance between the points (0, 7) and (8, 1)? (a) 10 (b) 11 (c) 100 (d) 14
  22. 22.In which quadrant does the point (−3, 3) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  23. 23.What is the distance between the points (6, 18) and (18, 9)? (a) 21 (b) 15 (c) 225 (d) 16
  24. 24.What is the midpoint of the line joining (4, 11) and (12, 7)? (a) (9, 8) (b) (4, 2) (c) (8, 9) (d) (16, 18)
  25. 25.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 31 (c) 25 (d) 625
  26. 26.In which quadrant does the point (−1, 4) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  27. 27.In which quadrant does the point (−3, 4) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  28. 28.In which quadrant does the point (4, 3) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  29. 29.What is the distance between the points (6, 9) and (21, 1)? (a) 289 (b) 17 (c) 18 (d) 23
  30. 30.In which quadrant does the point (9, 5) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  31. 31.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 14 (c) 13 (d) 17
  32. 32.What is the distance between the points (2, 15) and (10, 0)? (a) 23 (b) 18 (c) 289 (d) 17
  33. 33.In which quadrant does the point (6, 4) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  34. 34.What is the midpoint of the line joining (9, 10) and (11, 6)? (a) (10, 8) (b) (20, 16) (c) (8, 10) (d) (1, 2)
  35. 35.In which quadrant does the point (1, −1) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  36. 36.In which quadrant does the point (3, 2) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  37. 37.What is the distance between the points (0, 5) and (16, 17)? (a) 21 (b) 20 (c) 400 (d) 28
  38. 38.What is the distance between the points (0, 0) and (6, 8)? (a) 14 (b) 11 (c) 100 (d) 10
  39. 39.In which quadrant does the point (−2, 9) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  40. 40.What is the midpoint of the line joining (6, 8) and (10, 16)? (a) (16, 24) (b) (2, 4) (c) (12, 8) (d) (8, 12)

Answer key

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

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