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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 64 · 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.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 15 (c) 21 (d) 16
  2. 2.What is the distance between the points (4, 9) and (16, 18)? (a) 15 (b) 16 (c) 21 (d) 225
  3. 3.In which quadrant does the point (9, 5) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  4. 4.In which quadrant does the point (−5, −8) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  5. 5.What is the distance between the points (1, 15) and (9, 9)? (a) 14 (b) 10 (c) 100 (d) 11
  6. 6.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 10 (c) 11 (d) 14
  7. 7.What is the distance between the points (0, 8) and (12, 17)? (a) 21 (b) 16 (c) 15 (d) 225
  8. 8.What is the midpoint of the line joining (4, 14) and (6, 10)? (a) (10, 24) (b) (12, 5) (c) (1, 2) (d) (5, 12)
  9. 9.In which quadrant does the point (−8, −4) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  10. 10.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 10 (c) 14 (d) 100
  11. 11.What is the midpoint of the line joining (10, 7) and (12, 13)? (a) (11, 10) (b) (22, 20) (c) (10, 11) (d) (1, 3)
  12. 12.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 225 (c) 16 (d) 15
  13. 13.What is the distance between the points (7, 0) and (23, 12)? (a) 21 (b) 20 (c) 28 (d) 400
  14. 14.What is the distance between the points (4, 8) and (8, 5)? (a) 7 (b) 5 (c) 25 (d) 6
  15. 15.What is the midpoint of the line joining (4, 19) and (16, 9)? (a) (14, 10) (b) (6, 5) (c) (10, 14) (d) (20, 28)
  16. 16.In which quadrant does the point (−1, −4) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  17. 17.In which quadrant does the point (−1, 4) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  18. 18.What is the distance between the points (3, 13) and (9, 5)? (a) 100 (b) 11 (c) 10 (d) 14
  19. 19.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 20 (c) 400 (d) 21
  20. 20.What is the distance between the points (0, 3) and (8, 18)? (a) 23 (b) 289 (c) 18 (d) 17
  21. 21.What is the midpoint of the line joining (4, 15) and (6, 9)? (a) (5, 12) (b) (10, 24) (c) (1, 3) (d) (12, 5)
  22. 22.How far is the point (24, 7) from the origin (0, 0)? (a) 26 (b) 25 (c) 625 (d) 31
  23. 23.What is the midpoint of the line joining (2, 2) and (14, 8)? (a) (5, 8) (b) (16, 10) (c) (8, 5) (d) (6, 3)
  24. 24.What is the midpoint of the line joining (1, 19) and (7, 9)? (a) (8, 28) (b) (14, 4) (c) (3, 5) (d) (4, 14)
  25. 25.What is the distance between the points (8, 6) and (24, 18)? (a) 20 (b) 400 (c) 28 (d) 21
  26. 26.What is the distance between the points (9, 13) and (21, 8)? (a) 13 (b) 14 (c) 169 (d) 17
  27. 27.In which quadrant does the point (1, 3) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  28. 28.What is the midpoint of the line joining (2, 16) and (12, 6)? (a) (11, 7) (b) (5, 5) (c) (7, 11) (d) (14, 22)
  29. 29.What is the midpoint of the line joining (3, 14) and (15, 2)? (a) (8, 9) (b) (6, 6) (c) (9, 8) (d) (18, 16)
  30. 30.What is the distance between the points (3, 6) and (18, 14)? (a) 18 (b) 23 (c) 17 (d) 289
  31. 31.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 25 (c) 6 (d) 5
  32. 32.What is the midpoint of the line joining (10, 10) and (18, 2)? (a) (4, 4) (b) (6, 14) (c) (28, 12) (d) (14, 6)
  33. 33.What is the distance between the points (0, 5) and (8, 11)? (a) 11 (b) 14 (c) 100 (d) 10
  34. 34.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 7 (c) 25 (d) 5
  35. 35.What is the distance between the points (2, 17) and (8, 9)? (a) 100 (b) 14 (c) 10 (d) 11
  36. 36.What is the midpoint of the line joining (7, 8) and (9, 2)? (a) (5, 8) (b) (16, 10) (c) (8, 5) (d) (1, 3)
  37. 37.What is the distance between the points (1, 6) and (5, 9)? (a) 6 (b) 25 (c) 5 (d) 7
  38. 38.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 289 (c) 17 (d) 18
  39. 39.In which quadrant does the point (4, 5) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  40. 40.What is the midpoint of the line joining (3, 5) and (9, 3)? (a) (12, 8) (b) (6, 4) (c) (3, 1) (d) (4, 6)

Answer key

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

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