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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 720 · 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 (8, 0) and (14, 2)? (a) (22, 2) (b) (11, 1) (c) (3, 1) (d) (1, 11)
  2. 2.What is the distance between the points (7, 8) and (15, 23)? (a) 23 (b) 17 (c) 289 (d) 18
  3. 3.What is the distance between the points (0, 7) and (4, 10)? (a) 7 (b) 5 (c) 6 (d) 25
  4. 4.In which quadrant does the point (−7, −8) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  5. 5.In which quadrant does the point (−3, 4) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  6. 6.What is the distance between the points (6, 8) and (10, 5)? (a) 25 (b) 7 (c) 5 (d) 6
  7. 7.In which quadrant does the point (7, −5) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  8. 8.What is the midpoint of the line joining (10, 9) and (18, 13)? (a) (4, 2) (b) (28, 22) (c) (14, 11) (d) (11, 14)
  9. 9.What is the midpoint of the line joining (6, 8) and (18, 12)? (a) (10, 12) (b) (12, 10) (c) (24, 20) (d) (6, 2)
  10. 10.What is the midpoint of the line joining (8, 14) and (16, 8)? (a) (12, 11) (b) (11, 12) (c) (24, 22) (d) (4, 3)
  11. 11.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 15 (c) 16 (d) 21
  12. 12.What is the distance between the points (9, 4) and (15, 12)? (a) 11 (b) 14 (c) 100 (d) 10
  13. 13.What is the midpoint of the line joining (8, 12) and (10, 0)? (a) (6, 9) (b) (18, 12) (c) (1, 6) (d) (9, 6)
  14. 14.In which quadrant does the point (−6, −3) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  15. 15.What is the midpoint of the line joining (3, 14) and (7, 6)? (a) (10, 20) (b) (2, 4) (c) (10, 5) (d) (5, 10)
  16. 16.In which quadrant does the point (−6, 1) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  17. 17.In which quadrant does the point (−8, 3) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  18. 18.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 400 (c) 21 (d) 20
  19. 19.What is the distance between the points (9, 8) and (16, 32)? (a) 26 (b) 31 (c) 25 (d) 625
  20. 20.What is the midpoint of the line joining (4, 6) and (8, 12)? (a) (9, 6) (b) (6, 9) (c) (2, 3) (d) (12, 18)
  21. 21.What is the midpoint of the line joining (10, 6) and (18, 10)? (a) (14, 8) (b) (8, 14) (c) (4, 2) (d) (28, 16)
  22. 22.In which quadrant does the point (2, 8) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  23. 23.In which quadrant does the point (3, 8) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  24. 24.In which quadrant does the point (−9, 4) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  25. 25.What is the distance between the points (0, 13) and (5, 1)? (a) 169 (b) 13 (c) 17 (d) 14
  26. 26.What is the midpoint of the line joining (6, 3) and (10, 15)? (a) (9, 8) (b) (8, 9) (c) (2, 6) (d) (16, 18)
  27. 27.In which quadrant does the point (−7, −2) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  28. 28.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 5 (c) 7 (d) 6
  29. 29.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 14 (c) 10 (d) 100
  30. 30.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 625 (c) 26 (d) 25
  31. 31.What is the midpoint of the line joining (2, 15) and (10, 9)? (a) (12, 24) (b) (4, 3) (c) (6, 12) (d) (12, 6)
  32. 32.How far is the point (15, 8) from the origin (0, 0)? (a) 17 (b) 289 (c) 18 (d) 23
  33. 33.What is the midpoint of the line joining (3, 7) and (7, 5)? (a) (2, 1) (b) (10, 12) (c) (6, 5) (d) (5, 6)
  34. 34.How far is the point (24, 7) from the origin (0, 0)? (a) 25 (b) 26 (c) 31 (d) 625
  35. 35.In which quadrant does the point (−7, −3) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  36. 36.What is the distance between the points (2, 12) and (18, 0)? (a) 28 (b) 21 (c) 20 (d) 400
  37. 37.In which quadrant does the point (5, −5) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  38. 38.What is the distance between the points (6, 10) and (10, 7)? (a) 25 (b) 6 (c) 5 (d) 7
  39. 39.What is the distance between the points (7, 16) and (15, 1)? (a) 23 (b) 17 (c) 18 (d) 289
  40. 40.What is the distance between the points (3, 14) and (15, 5)? (a) 21 (b) 15 (c) 225 (d) 16

Answer key

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

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