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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 589 · 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 (8, 27) and (15, 3)? (a) 625 (b) 25 (c) 26 (d) 31
  2. 2.What is the distance between the points (4, 5) and (20, 17)? (a) 21 (b) 400 (c) 20 (d) 28
  3. 3.In which quadrant does the point (−7, −7) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  4. 4.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 400 (c) 20 (d) 21
  5. 5.What is the midpoint of the line joining (0, 5) and (12, 9)? (a) (7, 6) (b) (6, 7) (c) (6, 2) (d) (12, 14)
  6. 6.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 6 (c) 5 (d) 7
  7. 7.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 11 (c) 14 (d) 10
  8. 8.What is the midpoint of the line joining (8, 1) and (12, 7)? (a) (10, 4) (b) (2, 3) (c) (4, 10) (d) (20, 8)
  9. 9.What is the midpoint of the line joining (9, 6) and (11, 10)? (a) (20, 16) (b) (1, 2) (c) (8, 10) (d) (10, 8)
  10. 10.What is the midpoint of the line joining (6, 6) and (10, 8)? (a) (16, 14) (b) (2, 1) (c) (8, 7) (d) (7, 8)
  11. 11.What is the distance between the points (8, 14) and (17, 2)? (a) 21 (b) 225 (c) 15 (d) 16
  12. 12.In which quadrant does the point (4, −3) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  13. 13.What is the distance between the points (8, 17) and (16, 2)? (a) 17 (b) 23 (c) 18 (d) 289
  14. 14.How far is the point (16, 12) from the origin (0, 0)? (a) 400 (b) 20 (c) 21 (d) 28
  15. 15.What is the midpoint of the line joining (10, 20) and (16, 10)? (a) (3, 5) (b) (26, 30) (c) (13, 15) (d) (15, 13)
  16. 16.In which quadrant does the point (9, 9) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  17. 17.What is the distance between the points (5, 4) and (11, 12)? (a) 14 (b) 10 (c) 100 (d) 11
  18. 18.In which quadrant does the point (5, 8) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  19. 19.What is the midpoint of the line joining (1, 8) and (3, 10)? (a) (1, 1) (b) (9, 2) (c) (2, 9) (d) (4, 18)
  20. 20.What is the distance between the points (9, 8) and (33, 15)? (a) 26 (b) 31 (c) 25 (d) 625
  21. 21.What is the distance between the points (2, 5) and (14, 21)? (a) 21 (b) 400 (c) 20 (d) 28
  22. 22.What is the distance between the points (0, 3) and (8, 18)? (a) 18 (b) 289 (c) 17 (d) 23
  23. 23.What is the distance between the points (2, 8) and (26, 1)? (a) 26 (b) 625 (c) 31 (d) 25
  24. 24.What is the distance between the points (2, 16) and (14, 7)? (a) 16 (b) 15 (c) 225 (d) 21
  25. 25.What is the distance between the points (8, 25) and (15, 1)? (a) 26 (b) 31 (c) 625 (d) 25
  26. 26.What is the midpoint of the line joining (8, 4) and (12, 10)? (a) (7, 10) (b) (2, 3) (c) (10, 7) (d) (20, 14)
  27. 27.In which quadrant does the point (−2, 5) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  28. 28.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 15 (c) 16 (d) 225
  29. 29.What is the midpoint of the line joining (8, 11) and (14, 3)? (a) (3, 4) (b) (11, 7) (c) (22, 14) (d) (7, 11)
  30. 30.What is the midpoint of the line joining (6, 4) and (16, 6)? (a) (22, 10) (b) (11, 5) (c) (5, 11) (d) (5, 1)
  31. 31.What is the distance between the points (4, 15) and (20, 3)? (a) 400 (b) 21 (c) 20 (d) 28
  32. 32.What is the distance between the points (2, 1) and (18, 13)? (a) 400 (b) 20 (c) 28 (d) 21
  33. 33.In which quadrant does the point (9, 8) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  34. 34.In which quadrant does the point (9, 2) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  35. 35.In which quadrant does the point (−4, 8) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  36. 36.In which quadrant does the point (4, 3) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  37. 37.In which quadrant does the point (9, 6) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  38. 38.What is the midpoint of the line joining (9, 15) and (11, 7)? (a) (10, 11) (b) (1, 4) (c) (20, 22) (d) (11, 10)
  39. 39.In which quadrant does the point (−2, 3) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  40. 40.What is the distance between the points (2, 9) and (14, 4)? (a) 14 (b) 13 (c) 17 (d) 169

Answer key

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

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