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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 707 · 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, 4) and (4, 1)? (a) 7 (b) 25 (c) 6 (d) 5
  2. 2.What is the distance between the points (2, 3) and (26, 10)? (a) 26 (b) 625 (c) 25 (d) 31
  3. 3.What is the distance between the points (5, 13) and (17, 4)? (a) 225 (b) 15 (c) 16 (d) 21
  4. 4.What is the distance between the points (2, 0) and (14, 5)? (a) 13 (b) 17 (c) 169 (d) 14
  5. 5.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 11 (c) 100 (d) 14
  6. 6.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 5 (c) 25 (d) 6
  7. 7.In which quadrant does the point (3, −9) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  8. 8.In which quadrant does the point (2, 6) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  9. 9.How far is the point (16, 12) from the origin (0, 0)? (a) 400 (b) 20 (c) 21 (d) 28
  10. 10.What is the distance between the points (2, 7) and (6, 10)? (a) 6 (b) 5 (c) 7 (d) 25
  11. 11.What is the distance between the points (4, 8) and (7, 4)? (a) 6 (b) 25 (c) 7 (d) 5
  12. 12.What is the distance between the points (1, 5) and (4, 9)? (a) 25 (b) 6 (c) 5 (d) 7
  13. 13.In which quadrant does the point (9, 8) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  14. 14.How far is the point (7, 24) from the origin (0, 0)? (a) 25 (b) 31 (c) 625 (d) 26
  15. 15.What is the distance between the points (2, 2) and (17, 10)? (a) 23 (b) 17 (c) 289 (d) 18
  16. 16.In which quadrant does the point (5, 3) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  17. 17.What is the distance between the points (8, 2) and (20, 18)? (a) 20 (b) 400 (c) 21 (d) 28
  18. 18.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 14 (c) 10 (d) 11
  19. 19.What is the distance between the points (2, 7) and (5, 3)? (a) 6 (b) 25 (c) 5 (d) 7
  20. 20.In which quadrant does the point (9, −7) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  21. 21.What is the midpoint of the line joining (1, 4) and (5, 14)? (a) (3, 9) (b) (9, 3) (c) (2, 5) (d) (6, 18)
  22. 22.What is the midpoint of the line joining (7, 0) and (15, 4)? (a) (4, 2) (b) (22, 4) (c) (11, 2) (d) (2, 11)
  23. 23.What is the distance between the points (3, 2) and (10, 26)? (a) 31 (b) 625 (c) 25 (d) 26
  24. 24.What is the distance between the points (1, 18) and (6, 6)? (a) 13 (b) 169 (c) 14 (d) 17
  25. 25.What is the distance between the points (8, 2) and (17, 14)? (a) 225 (b) 16 (c) 15 (d) 21
  26. 26.What is the midpoint of the line joining (10, 3) and (12, 1)? (a) (11, 2) (b) (22, 4) (c) (2, 11) (d) (1, 1)
  27. 27.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 25 (c) 6 (d) 5
  28. 28.What is the distance between the points (7, 5) and (10, 1)? (a) 5 (b) 6 (c) 7 (d) 25
  29. 29.What is the distance between the points (6, 8) and (15, 20)? (a) 225 (b) 15 (c) 16 (d) 21
  30. 30.In which quadrant does the point (3, −1) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  31. 31.In which quadrant does the point (−2, 3) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  32. 32.What is the distance between the points (0, 7) and (5, 19)? (a) 169 (b) 14 (c) 13 (d) 17
  33. 33.What is the midpoint of the line joining (10, 5) and (16, 11)? (a) (3, 3) (b) (8, 13) (c) (13, 8) (d) (26, 16)
  34. 34.What is the midpoint of the line joining (4, 4) and (6, 6)? (a) (6, 5) (b) (5, 5) (c) (10, 10) (d) (1, 1)
  35. 35.What is the midpoint of the line joining (4, 7) and (6, 1)? (a) (10, 8) (b) (1, 3) (c) (4, 5) (d) (5, 4)
  36. 36.What is the distance between the points (2, 15) and (17, 7)? (a) 18 (b) 23 (c) 17 (d) 289
  37. 37.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 14 (c) 13 (d) 169
  38. 38.What is the midpoint of the line joining (6, 2) and (12, 14)? (a) (8, 9) (b) (18, 16) (c) (3, 6) (d) (9, 8)
  39. 39.In which quadrant does the point (3, −3) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  40. 40.What is the distance between the points (1, 2) and (5, 5)? (a) 25 (b) 5 (c) 7 (d) 6

Answer key

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

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