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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 480 · 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 midpoint of the line joining (1, 12) and (7, 10)? (a) (4, 11) (b) (3, 1) (c) (8, 22) (d) (11, 4)
  2. 2.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 28 (c) 400 (d) 21
  3. 3.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 289 (c) 23 (d) 18
  4. 4.What is the distance between the points (9, 7) and (12, 3)? (a) 6 (b) 5 (c) 7 (d) 25
  5. 5.What is the distance between the points (1, 16) and (13, 0)? (a) 20 (b) 21 (c) 28 (d) 400
  6. 6.In which quadrant does the point (6, −5) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  7. 7.What is the midpoint of the line joining (9, 11) and (11, 3)? (a) (1, 4) (b) (10, 7) (c) (7, 10) (d) (20, 14)
  8. 8.In which quadrant does the point (5, −3) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  9. 9.What is the midpoint of the line joining (3, 0) and (15, 4)? (a) (6, 2) (b) (9, 2) (c) (2, 9) (d) (18, 4)
  10. 10.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 5 (c) 7 (d) 25
  11. 11.What is the midpoint of the line joining (2, 13) and (12, 1)? (a) (5, 6) (b) (14, 14) (c) (7, 7) (d) (8, 7)
  12. 12.What is the distance between the points (7, 3) and (11, 6)? (a) 6 (b) 25 (c) 7 (d) 5
  13. 13.What is the distance between the points (7, 7) and (10, 11)? (a) 6 (b) 25 (c) 5 (d) 7
  14. 14.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 10 (c) 14 (d) 100
  15. 15.In which quadrant does the point (−9, −4) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  16. 16.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 16 (c) 21 (d) 15
  17. 17.In which quadrant does the point (2, 8) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  18. 18.In which quadrant does the point (3, −8) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  19. 19.In which quadrant does the point (−5, −1) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  20. 20.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 7 (c) 5 (d) 6
  21. 21.In which quadrant does the point (−8, 6) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  22. 22.What is the distance between the points (8, 5) and (16, 20)? (a) 289 (b) 18 (c) 23 (d) 17
  23. 23.What is the distance between the points (6, 2) and (18, 11)? (a) 225 (b) 16 (c) 21 (d) 15
  24. 24.In which quadrant does the point (8, 4) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  25. 25.What is the distance between the points (9, 1) and (13, 4)? (a) 25 (b) 5 (c) 7 (d) 6
  26. 26.In which quadrant does the point (−3, 6) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  27. 27.What is the distance between the points (0, 31) and (7, 7)? (a) 26 (b) 625 (c) 31 (d) 25
  28. 28.What is the distance between the points (9, 21) and (17, 6)? (a) 17 (b) 289 (c) 23 (d) 18
  29. 29.What is the distance between the points (6, 14) and (21, 6)? (a) 23 (b) 289 (c) 17 (d) 18
  30. 30.What is the midpoint of the line joining (3, 8) and (15, 2)? (a) (9, 5) (b) (5, 9) (c) (6, 3) (d) (18, 10)
  31. 31.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 11 (c) 100 (d) 14
  32. 32.In which quadrant does the point (5, −9) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  33. 33.In which quadrant does the point (5, 1) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  34. 34.What is the midpoint of the line joining (7, 6) and (19, 2)? (a) (26, 8) (b) (4, 13) (c) (6, 2) (d) (13, 4)
  35. 35.What is the distance between the points (0, 14) and (12, 9)? (a) 17 (b) 13 (c) 14 (d) 169
  36. 36.What is the midpoint of the line joining (4, 6) and (6, 10)? (a) (8, 5) (b) (1, 2) (c) (5, 8) (d) (10, 16)
  37. 37.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 17 (c) 169 (d) 13
  38. 38.What is the distance between the points (6, 7) and (15, 19)? (a) 15 (b) 21 (c) 225 (d) 16
  39. 39.What is the midpoint of the line joining (4, 1) and (6, 7)? (a) (5, 4) (b) (4, 5) (c) (1, 3) (d) (10, 8)
  40. 40.What is the midpoint of the line joining (7, 14) and (19, 4)? (a) (26, 18) (b) (13, 9) (c) (6, 5) (d) (9, 13)

Answer key

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

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