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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 759 · 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 (6, 6) and (12, 10)? (a) (18, 16) (b) (8, 9) (c) (3, 2) (d) (9, 8)
  2. 2.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 5 (c) 25 (d) 7
  3. 3.How far is the point (9, 12) from the origin (0, 0)? (a) 15 (b) 225 (c) 21 (d) 16
  4. 4.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 10 (c) 100 (d) 11
  5. 5.How far is the point (4, 3) from the origin (0, 0)? (a) 5 (b) 7 (c) 6 (d) 25
  6. 6.In which quadrant does the point (3, −2) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  7. 7.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 28 (c) 21 (d) 20
  8. 8.In which quadrant does the point (−8, −2) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  9. 9.What is the distance between the points (5, 11) and (8, 7)? (a) 25 (b) 6 (c) 5 (d) 7
  10. 10.What is the midpoint of the line joining (5, 3) and (15, 1)? (a) (5, 1) (b) (2, 10) (c) (10, 2) (d) (20, 4)
  11. 11.What is the midpoint of the line joining (3, 14) and (15, 10)? (a) (6, 2) (b) (9, 12) (c) (18, 24) (d) (12, 9)
  12. 12.What is the midpoint of the line joining (10, 17) and (20, 9)? (a) (5, 4) (b) (30, 26) (c) (13, 15) (d) (15, 13)
  13. 13.In which quadrant does the point (−4, −3) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  14. 14.What is the midpoint of the line joining (5, 7) and (11, 1)? (a) (3, 3) (b) (16, 8) (c) (8, 4) (d) (4, 8)
  15. 15.What is the midpoint of the line joining (4, 5) and (6, 13)? (a) (5, 9) (b) (1, 4) (c) (9, 5) (d) (10, 18)
  16. 16.What is the midpoint of the line joining (5, 13) and (13, 5)? (a) (9, 9) (b) (10, 9) (c) (18, 18) (d) (4, 4)
  17. 17.In which quadrant does the point (−9, 1) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  18. 18.What is the midpoint of the line joining (9, 3) and (13, 9)? (a) (11, 6) (b) (22, 12) (c) (6, 11) (d) (2, 3)
  19. 19.What is the midpoint of the line joining (9, 4) and (13, 12)? (a) (22, 16) (b) (11, 8) (c) (2, 4) (d) (8, 11)
  20. 20.What is the midpoint of the line joining (1, 7) and (3, 17)? (a) (12, 2) (b) (4, 24) (c) (2, 12) (d) (1, 5)
  21. 21.What is the distance between the points (1, 0) and (13, 16)? (a) 28 (b) 400 (c) 20 (d) 21
  22. 22.What is the distance between the points (8, 7) and (16, 13)? (a) 11 (b) 14 (c) 100 (d) 10
  23. 23.What is the midpoint of the line joining (1, 6) and (3, 16)? (a) (4, 22) (b) (2, 11) (c) (1, 5) (d) (11, 2)
  24. 24.What is the midpoint of the line joining (4, 3) and (10, 7)? (a) (3, 2) (b) (14, 10) (c) (5, 7) (d) (7, 5)
  25. 25.In which quadrant does the point (−6, −3) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  26. 26.What is the distance between the points (5, 9) and (20, 1)? (a) 18 (b) 289 (c) 17 (d) 23
  27. 27.What is the distance between the points (1, 8) and (25, 1)? (a) 26 (b) 625 (c) 31 (d) 25
  28. 28.In which quadrant does the point (8, 3) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  29. 29.In which quadrant does the point (7, 3) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  30. 30.What is the distance between the points (7, 16) and (15, 1)? (a) 289 (b) 17 (c) 23 (d) 18
  31. 31.What is the midpoint of the line joining (6, 4) and (8, 2)? (a) (1, 1) (b) (7, 3) (c) (14, 6) (d) (3, 7)
  32. 32.How far is the point (12, 9) from the origin (0, 0)? (a) 15 (b) 21 (c) 225 (d) 16
  33. 33.In which quadrant does the point (−3, −1) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  34. 34.In which quadrant does the point (−4, 3) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  35. 35.What is the distance between the points (6, 32) and (13, 8)? (a) 25 (b) 26 (c) 31 (d) 625
  36. 36.What is the midpoint of the line joining (9, 2) and (11, 6)? (a) (4, 10) (b) (20, 8) (c) (10, 4) (d) (1, 2)
  37. 37.What is the distance between the points (4, 2) and (20, 14)? (a) 400 (b) 21 (c) 20 (d) 28
  38. 38.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 14 (c) 13 (d) 17
  39. 39.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 14 (c) 10 (d) 100
  40. 40.What is the midpoint of the line joining (3, 4) and (7, 0)? (a) (2, 2) (b) (10, 4) (c) (5, 2) (d) (2, 5)

Answer key

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

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