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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 893 · 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 (0, 7) and (6, 15)? (a) 10 (b) 11 (c) 14 (d) 100
  2. 2.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 17 (c) 23 (d) 18
  3. 3.What is the midpoint of the line joining (3, 8) and (5, 6)? (a) (4, 7) (b) (8, 14) (c) (1, 1) (d) (7, 4)
  4. 4.What is the distance between the points (6, 5) and (18, 21)? (a) 400 (b) 20 (c) 28 (d) 21
  5. 5.What is the distance between the points (2, 5) and (5, 1)? (a) 5 (b) 25 (c) 6 (d) 7
  6. 6.What is the distance between the points (4, 7) and (28, 0)? (a) 25 (b) 625 (c) 31 (d) 26
  7. 7.What is the distance between the points (2, 12) and (5, 8)? (a) 5 (b) 25 (c) 7 (d) 6
  8. 8.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 5 (c) 6 (d) 7
  9. 9.In which quadrant does the point (7, 8) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  10. 10.What is the distance between the points (5, 16) and (20, 8)? (a) 23 (b) 17 (c) 289 (d) 18
  11. 11.What is the midpoint of the line joining (0, 11) and (4, 5)? (a) (4, 16) (b) (2, 3) (c) (8, 2) (d) (2, 8)
  12. 12.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 5 (c) 7 (d) 6
  13. 13.What is the distance between the points (9, 21) and (18, 9)? (a) 225 (b) 15 (c) 16 (d) 21
  14. 14.What is the midpoint of the line joining (3, 7) and (13, 3)? (a) (16, 10) (b) (5, 8) (c) (8, 5) (d) (5, 2)
  15. 15.What is the distance between the points (8, 4) and (15, 28)? (a) 25 (b) 625 (c) 26 (d) 31
  16. 16.What is the distance between the points (2, 1) and (8, 9)? (a) 14 (b) 100 (c) 11 (d) 10
  17. 17.What is the distance between the points (5, 4) and (8, 8)? (a) 25 (b) 7 (c) 5 (d) 6
  18. 18.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 289 (c) 17 (d) 18
  19. 19.In which quadrant does the point (−1, 1) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  20. 20.How far is the point (24, 7) from the origin (0, 0)? (a) 26 (b) 31 (c) 625 (d) 25
  21. 21.What is the distance between the points (7, 17) and (15, 2)? (a) 289 (b) 18 (c) 23 (d) 17
  22. 22.What is the distance between the points (3, 10) and (15, 1)? (a) 16 (b) 225 (c) 21 (d) 15
  23. 23.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 31 (c) 25 (d) 625
  24. 24.What is the midpoint of the line joining (5, 5) and (17, 1)? (a) (6, 2) (b) (3, 11) (c) (11, 3) (d) (22, 6)
  25. 25.In which quadrant does the point (6, 9) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  26. 26.What is the midpoint of the line joining (4, 16) and (6, 6)? (a) (11, 5) (b) (5, 11) (c) (10, 22) (d) (1, 5)
  27. 27.In which quadrant does the point (3, 5) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  28. 28.What is the midpoint of the line joining (7, 10) and (11, 18)? (a) (2, 4) (b) (18, 28) (c) (14, 9) (d) (9, 14)
  29. 29.In which quadrant does the point (5, −7) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  30. 30.What is the distance between the points (1, 11) and (7, 3)? (a) 11 (b) 100 (c) 10 (d) 14
  31. 31.What is the midpoint of the line joining (0, 9) and (2, 5)? (a) (1, 7) (b) (7, 1) (c) (2, 14) (d) (1, 2)
  32. 32.What is the distance between the points (6, 22) and (18, 6)? (a) 20 (b) 400 (c) 28 (d) 21
  33. 33.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 400 (c) 21 (d) 28
  34. 34.What is the distance between the points (2, 2) and (10, 8)? (a) 14 (b) 100 (c) 10 (d) 11
  35. 35.What is the distance between the points (4, 4) and (19, 12)? (a) 289 (b) 18 (c) 23 (d) 17
  36. 36.What is the midpoint of the line joining (7, 6) and (13, 18)? (a) (12, 10) (b) (3, 6) (c) (20, 24) (d) (10, 12)
  37. 37.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 15 (c) 21 (d) 225
  38. 38.What is the distance between the points (7, 2) and (10, 6)? (a) 6 (b) 25 (c) 5 (d) 7
  39. 39.In which quadrant does the point (−6, 8) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  40. 40.In which quadrant does the point (−1, −2) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant

Answer key

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

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