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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 806 · 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 (0, 7) and (2, 9)? (a) (1, 8) (b) (1, 1) (c) (8, 1) (d) (2, 16)
  2. 2.In which quadrant does the point (8, −2) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  3. 3.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 289 (c) 18 (d) 17
  4. 4.What is the midpoint of the line joining (4, 14) and (16, 4)? (a) (9, 10) (b) (20, 18) (c) (6, 5) (d) (10, 9)
  5. 5.In which quadrant does the point (−3, 1) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  6. 6.In which quadrant does the point (6, 2) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  7. 7.In which quadrant does the point (6, −9) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  8. 8.What is the distance between the points (6, 16) and (22, 4)? (a) 28 (b) 21 (c) 20 (d) 400
  9. 9.What is the distance between the points (8, 10) and (32, 3)? (a) 31 (b) 25 (c) 625 (d) 26
  10. 10.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 11 (c) 100 (d) 10
  11. 11.In which quadrant does the point (8, −7) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  12. 12.What is the midpoint of the line joining (3, 4) and (5, 12)? (a) (8, 16) (b) (1, 4) (c) (8, 4) (d) (4, 8)
  13. 13.What is the midpoint of the line joining (2, 18) and (10, 6)? (a) (12, 6) (b) (6, 12) (c) (12, 24) (d) (4, 6)
  14. 14.What is the distance between the points (6, 1) and (10, 4)? (a) 5 (b) 7 (c) 25 (d) 6
  15. 15.What is the midpoint of the line joining (3, 10) and (15, 14)? (a) (6, 2) (b) (9, 12) (c) (12, 9) (d) (18, 24)
  16. 16.How far is the point (12, 5) from the origin (0, 0)? (a) 13 (b) 14 (c) 169 (d) 17
  17. 17.What is the distance between the points (2, 0) and (14, 16)? (a) 21 (b) 400 (c) 20 (d) 28
  18. 18.What is the distance between the points (4, 4) and (7, 0)? (a) 5 (b) 25 (c) 7 (d) 6
  19. 19.In which quadrant does the point (−7, −3) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  20. 20.What is the midpoint of the line joining (1, 9) and (13, 15)? (a) (7, 12) (b) (14, 24) (c) (12, 7) (d) (6, 3)
  21. 21.What is the distance between the points (0, 3) and (6, 11)? (a) 11 (b) 14 (c) 10 (d) 100
  22. 22.What is the distance between the points (8, 5) and (11, 9)? (a) 5 (b) 6 (c) 7 (d) 25
  23. 23.What is the distance between the points (1, 3) and (9, 18)? (a) 18 (b) 17 (c) 289 (d) 23
  24. 24.What is the distance between the points (2, 14) and (10, 8)? (a) 100 (b) 14 (c) 10 (d) 11
  25. 25.What is the midpoint of the line joining (10, 3) and (14, 11)? (a) (12, 7) (b) (2, 4) (c) (24, 14) (d) (7, 12)
  26. 26.What is the midpoint of the line joining (0, 3) and (8, 11)? (a) (7, 4) (b) (8, 14) (c) (4, 4) (d) (4, 7)
  27. 27.In which quadrant does the point (−5, 9) 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) 225 (c) 15 (d) 16
  29. 29.What is the midpoint of the line joining (2, 11) and (10, 5)? (a) (6, 8) (b) (4, 3) (c) (8, 6) (d) (12, 16)
  30. 30.What is the midpoint of the line joining (3, 13) and (11, 1)? (a) (8, 7) (b) (14, 14) (c) (4, 6) (d) (7, 7)
  31. 31.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 14 (c) 11 (d) 10
  32. 32.What is the midpoint of the line joining (1, 1) and (11, 3)? (a) (5, 1) (b) (2, 6) (c) (12, 4) (d) (6, 2)
  33. 33.What is the midpoint of the line joining (9, 8) and (17, 14)? (a) (4, 3) (b) (26, 22) (c) (11, 13) (d) (13, 11)
  34. 34.What is the distance between the points (1, 11) and (9, 5)? (a) 14 (b) 100 (c) 11 (d) 10
  35. 35.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 26 (c) 31 (d) 25
  36. 36.What is the midpoint of the line joining (3, 14) and (7, 8)? (a) (2, 3) (b) (10, 22) (c) (5, 11) (d) (11, 5)
  37. 37.What is the midpoint of the line joining (6, 6) and (10, 14)? (a) (8, 10) (b) (2, 4) (c) (16, 20) (d) (10, 8)
  38. 38.In which quadrant does the point (−6, 3) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  39. 39.In which quadrant does the point (2, −5) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  40. 40.What is the distance between the points (6, 7) and (15, 19)? (a) 225 (b) 15 (c) 21 (d) 16

Answer key

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

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