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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 785 · 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 (5, 5) and (9, 15)? (a) (10, 7) (b) (2, 5) (c) (7, 10) (d) (14, 20)
  2. 2.In which quadrant does the point (2, 2) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  3. 3.In which quadrant does the point (−1, 2) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  4. 4.In which quadrant does the point (4, 3) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  5. 5.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 17 (c) 289 (d) 18
  6. 6.What is the midpoint of the line joining (3, 5) and (11, 15)? (a) (10, 7) (b) (4, 5) (c) (7, 10) (d) (14, 20)
  7. 7.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 16 (c) 225 (d) 15
  8. 8.What is the distance between the points (6, 1) and (11, 13)? (a) 17 (b) 13 (c) 169 (d) 14
  9. 9.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 13 (c) 14 (d) 17
  10. 10.What is the distance between the points (2, 8) and (26, 15)? (a) 31 (b) 625 (c) 26 (d) 25
  11. 11.What is the distance between the points (7, 17) and (13, 9)? (a) 11 (b) 10 (c) 14 (d) 100
  12. 12.What is the midpoint of the line joining (0, 14) and (6, 8)? (a) (11, 3) (b) (3, 3) (c) (6, 22) (d) (3, 11)
  13. 13.What is the midpoint of the line joining (6, 4) and (12, 2)? (a) (3, 9) (b) (9, 3) (c) (18, 6) (d) (3, 1)
  14. 14.What is the midpoint of the line joining (0, 0) and (6, 12)? (a) (6, 3) (b) (6, 12) (c) (4, 6) (d) (3, 6)
  15. 15.What is the distance between the points (2, 1) and (8, 9)? (a) 100 (b) 11 (c) 14 (d) 10
  16. 16.What is the distance between the points (8, 13) and (13, 1)? (a) 14 (b) 169 (c) 13 (d) 17
  17. 17.What is the distance between the points (4, 2) and (12, 8)? (a) 10 (b) 14 (c) 100 (d) 11
  18. 18.What is the distance between the points (7, 18) and (12, 6)? (a) 169 (b) 13 (c) 17 (d) 14
  19. 19.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 225 (c) 16 (d) 15
  20. 20.In which quadrant does the point (1, −5) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  21. 21.What is the midpoint of the line joining (9, 9) and (13, 3)? (a) (2, 3) (b) (11, 6) (c) (22, 12) (d) (6, 11)
  22. 22.What is the distance between the points (1, 14) and (10, 2)? (a) 225 (b) 21 (c) 16 (d) 15
  23. 23.In which quadrant does the point (1, 6) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  24. 24.In which quadrant does the point (9, 6) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  25. 25.In which quadrant does the point (5, −9) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  26. 26.What is the midpoint of the line joining (10, 5) and (16, 1)? (a) (3, 2) (b) (13, 3) (c) (26, 6) (d) (3, 13)
  27. 27.What is the distance between the points (2, 8) and (5, 4)? (a) 5 (b) 7 (c) 6 (d) 25
  28. 28.What is the midpoint of the line joining (6, 0) and (16, 8)? (a) (5, 4) (b) (4, 11) (c) (22, 8) (d) (11, 4)
  29. 29.What is the distance between the points (6, 8) and (10, 11)? (a) 6 (b) 5 (c) 7 (d) 25
  30. 30.How far is the point (7, 24) from the origin (0, 0)? (a) 25 (b) 31 (c) 26 (d) 625
  31. 31.How far is the point (4, 3) from the origin (0, 0)? (a) 5 (b) 25 (c) 6 (d) 7
  32. 32.What is the distance between the points (9, 2) and (14, 14)? (a) 13 (b) 17 (c) 169 (d) 14
  33. 33.What is the midpoint of the line joining (10, 0) and (18, 4)? (a) (28, 4) (b) (14, 2) (c) (4, 2) (d) (2, 14)
  34. 34.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 400 (c) 20 (d) 28
  35. 35.What is the midpoint of the line joining (0, 15) and (4, 3)? (a) (2, 6) (b) (4, 18) (c) (2, 9) (d) (9, 2)
  36. 36.What is the midpoint of the line joining (10, 5) and (16, 15)? (a) (10, 13) (b) (3, 5) (c) (13, 10) (d) (26, 20)
  37. 37.In which quadrant does the point (−3, −8) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  38. 38.What is the midpoint of the line joining (8, 10) and (10, 22)? (a) (1, 6) (b) (18, 32) (c) (16, 9) (d) (9, 16)
  39. 39.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 14 (c) 11 (d) 100
  40. 40.How far is the point (15, 8) from the origin (0, 0)? (a) 17 (b) 18 (c) 23 (d) 289

Answer key

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

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