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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 710 · 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 (1, 1) and (9, 16)? (a) 18 (b) 23 (c) 17 (d) 289
  2. 2.What is the distance between the points (4, 5) and (11, 29)? (a) 31 (b) 26 (c) 625 (d) 25
  3. 3.What is the distance between the points (6, 2) and (12, 10)? (a) 10 (b) 11 (c) 14 (d) 100
  4. 4.What is the midpoint of the line joining (3, 2) and (7, 10)? (a) (5, 6) (b) (10, 12) (c) (2, 4) (d) (6, 5)
  5. 5.What is the distance between the points (5, 2) and (14, 14)? (a) 15 (b) 21 (c) 225 (d) 16
  6. 6.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 15 (c) 16 (d) 225
  7. 7.What is the distance between the points (5, 21) and (13, 6)? (a) 289 (b) 17 (c) 18 (d) 23
  8. 8.What is the midpoint of the line joining (6, 15) and (8, 5)? (a) (1, 5) (b) (10, 7) (c) (7, 10) (d) (14, 20)
  9. 9.What is the midpoint of the line joining (2, 6) and (4, 4)? (a) (5, 3) (b) (6, 10) (c) (3, 5) (d) (1, 1)
  10. 10.What is the distance between the points (5, 9) and (11, 1)? (a) 100 (b) 11 (c) 10 (d) 14
  11. 11.What is the distance between the points (4, 1) and (13, 13)? (a) 16 (b) 21 (c) 225 (d) 15
  12. 12.What is the midpoint of the line joining (10, 5) and (22, 1)? (a) (16, 3) (b) (3, 16) (c) (32, 6) (d) (6, 2)
  13. 13.In which quadrant does the point (7, −5) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  14. 14.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 100 (c) 14 (d) 11
  15. 15.What is the distance between the points (3, 6) and (7, 3)? (a) 6 (b) 7 (c) 25 (d) 5
  16. 16.How far is the point (12, 5) from the origin (0, 0)? (a) 13 (b) 169 (c) 14 (d) 17
  17. 17.What is the distance between the points (4, 1) and (19, 9)? (a) 17 (b) 18 (c) 23 (d) 289
  18. 18.In which quadrant does the point (3, 1) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  19. 19.What is the midpoint of the line joining (4, 5) and (8, 17)? (a) (12, 22) (b) (11, 6) (c) (2, 6) (d) (6, 11)
  20. 20.What is the distance between the points (3, 11) and (9, 3)? (a) 100 (b) 11 (c) 14 (d) 10
  21. 21.What is the midpoint of the line joining (5, 14) and (15, 8)? (a) (11, 10) (b) (10, 11) (c) (20, 22) (d) (5, 3)
  22. 22.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 13 (c) 17 (d) 169
  23. 23.What is the midpoint of the line joining (8, 4) and (12, 16)? (a) (2, 6) (b) (11, 10) (c) (10, 10) (d) (20, 20)
  24. 24.In which quadrant does the point (5, 6) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  25. 25.What is the distance between the points (7, 3) and (31, 10)? (a) 625 (b) 31 (c) 26 (d) 25
  26. 26.In which quadrant does the point (−7, 2) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  27. 27.In which quadrant does the point (−1, −2) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  28. 28.In which quadrant does the point (−2, 5) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  29. 29.What is the distance between the points (4, 1) and (16, 10)? (a) 16 (b) 15 (c) 21 (d) 225
  30. 30.In which quadrant does the point (5, −2) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  31. 31.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 625 (c) 25 (d) 26
  32. 32.What is the distance between the points (0, 9) and (24, 16)? (a) 25 (b) 31 (c) 625 (d) 26
  33. 33.In which quadrant does the point (−4, −7) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  34. 34.What is the distance between the points (8, 17) and (23, 9)? (a) 18 (b) 289 (c) 17 (d) 23
  35. 35.In which quadrant does the point (7, 8) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  36. 36.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 21 (c) 400 (d) 20
  37. 37.What is the midpoint of the line joining (8, 2) and (10, 12)? (a) (7, 9) (b) (1, 5) (c) (18, 14) (d) (9, 7)
  38. 38.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 14 (c) 100 (d) 11
  39. 39.In which quadrant does the point (1, 6) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  40. 40.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 289 (c) 17 (d) 18

Answer key

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

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