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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 221 · 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 distance between the points (9, 5) and (13, 2)? (a) 5 (b) 25 (c) 7 (d) 6
  2. 2.What is the midpoint of the line joining (10, 3) and (14, 1)? (a) (2, 1) (b) (2, 12) (c) (12, 2) (d) (24, 4)
  3. 3.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 14 (c) 100 (d) 10
  4. 4.What is the midpoint of the line joining (0, 6) and (8, 16)? (a) (4, 5) (b) (4, 11) (c) (11, 4) (d) (8, 22)
  5. 5.What is the midpoint of the line joining (9, 6) and (11, 14)? (a) (11, 10) (b) (1, 4) (c) (20, 20) (d) (10, 10)
  6. 6.In which quadrant does the point (−7, −1) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  7. 7.What is the distance between the points (6, 3) and (11, 15)? (a) 14 (b) 13 (c) 169 (d) 17
  8. 8.In which quadrant does the point (−1, 5) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  9. 9.What is the distance between the points (4, 20) and (9, 8)? (a) 14 (b) 169 (c) 13 (d) 17
  10. 10.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 26 (c) 25 (d) 31
  11. 11.What is the midpoint of the line joining (8, 1) and (14, 13)? (a) (7, 11) (b) (22, 14) (c) (3, 6) (d) (11, 7)
  12. 12.What is the midpoint of the line joining (9, 9) and (11, 5)? (a) (10, 7) (b) (20, 14) (c) (1, 2) (d) (7, 10)
  13. 13.How far is the point (12, 5) from the origin (0, 0)? (a) 13 (b) 169 (c) 14 (d) 17
  14. 14.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 289 (c) 18 (d) 23
  15. 15.What is the distance between the points (5, 15) and (17, 6)? (a) 15 (b) 225 (c) 21 (d) 16
  16. 16.What is the midpoint of the line joining (1, 2) and (7, 8)? (a) (8, 10) (b) (5, 4) (c) (3, 3) (d) (4, 5)
  17. 17.What is the distance between the points (7, 1) and (23, 13)? (a) 400 (b) 28 (c) 21 (d) 20
  18. 18.What is the distance between the points (6, 16) and (22, 4)? (a) 28 (b) 20 (c) 400 (d) 21
  19. 19.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 6 (c) 7 (d) 5
  20. 20.What is the midpoint of the line joining (5, 1) and (15, 7)? (a) (20, 8) (b) (5, 3) (c) (10, 4) (d) (4, 10)
  21. 21.In which quadrant does the point (−1, −7) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  22. 22.In which quadrant does the point (7, 1) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  23. 23.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 6 (c) 7 (d) 5
  24. 24.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 21 (c) 15 (d) 16
  25. 25.In which quadrant does the point (9, −2) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  26. 26.What is the distance between the points (0, 22) and (8, 7)? (a) 18 (b) 289 (c) 17 (d) 23
  27. 27.What is the distance between the points (4, 8) and (28, 15)? (a) 25 (b) 26 (c) 625 (d) 31
  28. 28.What is the midpoint of the line joining (8, 6) and (14, 4)? (a) (5, 11) (b) (22, 10) (c) (11, 5) (d) (3, 1)
  29. 29.What is the distance between the points (2, 8) and (14, 13)? (a) 169 (b) 14 (c) 13 (d) 17
  30. 30.In which quadrant does the point (6, −9) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  31. 31.What is the distance between the points (8, 7) and (16, 13)? (a) 10 (b) 11 (c) 14 (d) 100
  32. 32.What is the midpoint of the line joining (1, 18) and (9, 6)? (a) (12, 5) (b) (5, 12) (c) (10, 24) (d) (4, 6)
  33. 33.In which quadrant does the point (3, −9) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  34. 34.What is the distance between the points (2, 9) and (18, 21)? (a) 400 (b) 21 (c) 28 (d) 20
  35. 35.What is the distance between the points (4, 5) and (28, 12)? (a) 31 (b) 26 (c) 25 (d) 625
  36. 36.What is the distance between the points (5, 7) and (9, 10)? (a) 25 (b) 5 (c) 6 (d) 7
  37. 37.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 31 (c) 26 (d) 25
  38. 38.In which quadrant does the point (−3, 1) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  39. 39.What is the midpoint of the line joining (0, 9) and (4, 11)? (a) (2, 10) (b) (2, 1) (c) (10, 2) (d) (4, 20)
  40. 40.What is the midpoint of the line joining (3, 2) and (11, 6)? (a) (14, 8) (b) (4, 7) (c) (4, 2) (d) (7, 4)

Answer key

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

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