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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 504 · 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 (3, 4) from the origin (0, 0)? (a) 7 (b) 5 (c) 25 (d) 6
  2. 2.What is the midpoint of the line joining (8, 13) and (10, 5)? (a) (10, 9) (b) (18, 18) (c) (9, 9) (d) (1, 4)
  3. 3.What is the distance between the points (2, 16) and (7, 4)? (a) 13 (b) 17 (c) 14 (d) 169
  4. 4.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 100 (c) 11 (d) 10
  5. 5.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 18 (c) 23 (d) 289
  6. 6.How far is the point (4, 3) from the origin (0, 0)? (a) 5 (b) 6 (c) 7 (d) 25
  7. 7.What is the midpoint of the line joining (1, 7) and (7, 11)? (a) (3, 2) (b) (9, 4) (c) (4, 9) (d) (8, 18)
  8. 8.In which quadrant does the point (−8, 2) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  9. 9.In which quadrant does the point (4, 1) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  10. 10.What is the distance between the points (4, 13) and (20, 1)? (a) 400 (b) 28 (c) 21 (d) 20
  11. 11.In which quadrant does the point (−9, −2) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  12. 12.What is the midpoint of the line joining (8, 15) and (14, 9)? (a) (3, 3) (b) (12, 11) (c) (11, 12) (d) (22, 24)
  13. 13.What is the midpoint of the line joining (5, 5) and (11, 7)? (a) (8, 6) (b) (16, 12) (c) (6, 8) (d) (3, 1)
  14. 14.What is the distance between the points (6, 11) and (21, 3)? (a) 23 (b) 18 (c) 17 (d) 289
  15. 15.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 11 (c) 100 (d) 14
  16. 16.What is the distance between the points (6, 3) and (12, 11)? (a) 10 (b) 100 (c) 11 (d) 14
  17. 17.In which quadrant does the point (5, −5) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  18. 18.What is the midpoint of the line joining (9, 2) and (15, 8)? (a) (12, 5) (b) (3, 3) (c) (5, 12) (d) (24, 10)
  19. 19.What is the midpoint of the line joining (2, 4) and (12, 16)? (a) (7, 10) (b) (10, 7) (c) (5, 6) (d) (14, 20)
  20. 20.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 17 (c) 289 (d) 23
  21. 21.In which quadrant does the point (−7, 4) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  22. 22.What is the midpoint of the line joining (9, 7) and (13, 15)? (a) (22, 22) (b) (12, 11) (c) (2, 4) (d) (11, 11)
  23. 23.How far is the point (24, 7) from the origin (0, 0)? (a) 26 (b) 31 (c) 25 (d) 625
  24. 24.What is the distance between the points (0, 5) and (16, 17)? (a) 21 (b) 28 (c) 20 (d) 400
  25. 25.What is the midpoint of the line joining (5, 11) and (11, 9)? (a) (3, 1) (b) (8, 10) (c) (10, 8) (d) (16, 20)
  26. 26.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 169 (c) 17 (d) 13
  27. 27.What is the midpoint of the line joining (8, 0) and (14, 6)? (a) (22, 6) (b) (3, 11) (c) (11, 3) (d) (3, 3)
  28. 28.In which quadrant does the point (1, −5) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  29. 29.What is the distance between the points (2, 23) and (14, 7)? (a) 21 (b) 20 (c) 28 (d) 400
  30. 30.What is the midpoint of the line joining (3, 13) and (7, 3)? (a) (5, 8) (b) (10, 16) (c) (8, 5) (d) (2, 5)
  31. 31.What is the distance between the points (6, 7) and (14, 1)? (a) 11 (b) 10 (c) 14 (d) 100
  32. 32.In which quadrant does the point (9, −1) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  33. 33.What is the distance between the points (4, 15) and (9, 3)? (a) 13 (b) 14 (c) 17 (d) 169
  34. 34.In which quadrant does the point (−4, 1) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  35. 35.What is the distance between the points (5, 19) and (13, 4)? (a) 289 (b) 18 (c) 23 (d) 17
  36. 36.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 21 (c) 20 (d) 28
  37. 37.How far is the point (16, 12) from the origin (0, 0)? (a) 400 (b) 20 (c) 21 (d) 28
  38. 38.What is the distance between the points (0, 15) and (24, 8)? (a) 625 (b) 26 (c) 25 (d) 31
  39. 39.What is the midpoint of the line joining (9, 9) and (15, 5)? (a) (3, 2) (b) (24, 14) (c) (7, 12) (d) (12, 7)
  40. 40.In which quadrant does the point (5, 1) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant

Answer key

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

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