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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 494 · 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 (4, 8) and (6, 10)? (a) (9, 5) (b) (1, 1) (c) (10, 18) (d) (5, 9)
  2. 2.What is the distance between the points (3, 8) and (15, 13)? (a) 17 (b) 169 (c) 14 (d) 13
  3. 3.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 20 (c) 28 (d) 21
  4. 4.What is the distance between the points (3, 7) and (19, 19)? (a) 400 (b) 28 (c) 20 (d) 21
  5. 5.How far is the point (15, 8) from the origin (0, 0)? (a) 17 (b) 18 (c) 23 (d) 289
  6. 6.In which quadrant does the point (5, 8) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  7. 7.In which quadrant does the point (−7, −2) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  8. 8.What is the midpoint of the line joining (4, 7) and (6, 11)? (a) (1, 2) (b) (9, 5) (c) (10, 18) (d) (5, 9)
  9. 9.What is the distance between the points (0, 7) and (6, 15)? (a) 10 (b) 14 (c) 11 (d) 100
  10. 10.What is the distance between the points (9, 7) and (15, 15)? (a) 14 (b) 10 (c) 11 (d) 100
  11. 11.What is the midpoint of the line joining (9, 8) and (21, 0)? (a) (6, 4) (b) (4, 15) (c) (30, 8) (d) (15, 4)
  12. 12.What is the distance between the points (4, 6) and (9, 18)? (a) 17 (b) 169 (c) 13 (d) 14
  13. 13.What is the distance between the points (0, 3) and (6, 11)? (a) 11 (b) 10 (c) 100 (d) 14
  14. 14.What is the distance between the points (7, 2) and (23, 14)? (a) 20 (b) 21 (c) 28 (d) 400
  15. 15.What is the midpoint of the line joining (6, 5) and (14, 3)? (a) (4, 1) (b) (10, 4) (c) (4, 10) (d) (20, 8)
  16. 16.What is the distance between the points (2, 12) and (5, 8)? (a) 5 (b) 6 (c) 7 (d) 25
  17. 17.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 5 (c) 6 (d) 7
  18. 18.In which quadrant does the point (−8, −7) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  19. 19.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 14 (c) 10 (d) 11
  20. 20.What is the midpoint of the line joining (5, 14) and (15, 4)? (a) (20, 18) (b) (9, 10) (c) (10, 9) (d) (5, 5)
  21. 21.What is the midpoint of the line joining (9, 12) and (11, 2)? (a) (10, 7) (b) (1, 5) (c) (7, 10) (d) (20, 14)
  22. 22.In which quadrant does the point (2, −1) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  23. 23.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 15 (c) 225 (d) 21
  24. 24.What is the midpoint of the line joining (4, 10) and (16, 16)? (a) (10, 13) (b) (13, 10) (c) (20, 26) (d) (6, 3)
  25. 25.What is the midpoint of the line joining (7, 6) and (15, 12)? (a) (11, 9) (b) (22, 18) (c) (9, 11) (d) (4, 3)
  26. 26.In which quadrant does the point (−4, −2) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  27. 27.In which quadrant does the point (8, 4) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  28. 28.In which quadrant does the point (−2, 1) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  29. 29.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 17 (c) 18 (d) 23
  30. 30.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 14 (c) 17 (d) 13
  31. 31.In which quadrant does the point (1, 3) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  32. 32.What is the midpoint of the line joining (6, 5) and (16, 17)? (a) (5, 6) (b) (12, 11) (c) (11, 11) (d) (22, 22)
  33. 33.In which quadrant does the point (−7, 8) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  34. 34.What is the distance between the points (9, 5) and (13, 2)? (a) 25 (b) 6 (c) 7 (d) 5
  35. 35.What is the distance between the points (8, 7) and (32, 14)? (a) 31 (b) 26 (c) 625 (d) 25
  36. 36.In which quadrant does the point (−1, 1) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  37. 37.What is the distance between the points (4, 7) and (12, 1)? (a) 11 (b) 14 (c) 100 (d) 10
  38. 38.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 11 (c) 100 (d) 10
  39. 39.What is the distance between the points (1, 14) and (9, 8)? (a) 100 (b) 10 (c) 11 (d) 14
  40. 40.In which quadrant does the point (1, 9) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant

Answer key

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

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