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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 571 · 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 (3, 9) and (18, 17)? (a) 18 (b) 289 (c) 17 (d) 23
  2. 2.What is the distance between the points (8, 2) and (20, 18)? (a) 400 (b) 21 (c) 28 (d) 20
  3. 3.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 15 (c) 21 (d) 16
  4. 4.In which quadrant does the point (5, 7) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  5. 5.What is the distance between the points (2, 3) and (14, 12)? (a) 225 (b) 15 (c) 16 (d) 21
  6. 6.What is the distance between the points (5, 8) and (9, 11)? (a) 7 (b) 5 (c) 6 (d) 25
  7. 7.What is the midpoint of the line joining (10, 6) and (18, 0)? (a) (14, 3) (b) (3, 14) (c) (28, 6) (d) (4, 3)
  8. 8.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 169 (c) 13 (d) 14
  9. 9.What is the distance between the points (9, 8) and (33, 15)? (a) 25 (b) 26 (c) 625 (d) 31
  10. 10.What is the midpoint of the line joining (6, 3) and (12, 15)? (a) (3, 6) (b) (10, 9) (c) (18, 18) (d) (9, 9)
  11. 11.What is the midpoint of the line joining (10, 10) and (12, 8)? (a) (11, 9) (b) (9, 11) (c) (22, 18) (d) (1, 1)
  12. 12.In which quadrant does the point (−6, 9) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  13. 13.What is the distance between the points (9, 2) and (15, 10)? (a) 11 (b) 10 (c) 100 (d) 14
  14. 14.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 100 (c) 10 (d) 14
  15. 15.In which quadrant does the point (−3, −9) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  16. 16.In which quadrant does the point (6, −8) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  17. 17.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 23 (c) 289 (d) 18
  18. 18.What is the distance between the points (4, 9) and (12, 24)? (a) 18 (b) 289 (c) 23 (d) 17
  19. 19.In which quadrant does the point (−4, 2) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  20. 20.How far is the point (12, 5) from the origin (0, 0)? (a) 13 (b) 17 (c) 14 (d) 169
  21. 21.What is the distance between the points (8, 6) and (12, 9)? (a) 7 (b) 25 (c) 5 (d) 6
  22. 22.What is the midpoint of the line joining (1, 1) and (7, 13)? (a) (3, 6) (b) (7, 4) (c) (8, 14) (d) (4, 7)
  23. 23.What is the distance between the points (5, 6) and (9, 3)? (a) 7 (b) 25 (c) 6 (d) 5
  24. 24.What is the distance between the points (2, 16) and (10, 1)? (a) 17 (b) 18 (c) 23 (d) 289
  25. 25.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 25 (c) 7 (d) 6
  26. 26.What is the midpoint of the line joining (10, 10) and (18, 8)? (a) (28, 18) (b) (4, 1) (c) (9, 14) (d) (14, 9)
  27. 27.What is the distance between the points (3, 7) and (11, 1)? (a) 100 (b) 11 (c) 10 (d) 14
  28. 28.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 11 (c) 14 (d) 100
  29. 29.What is the midpoint of the line joining (6, 10) and (16, 8)? (a) (11, 9) (b) (5, 1) (c) (9, 11) (d) (22, 18)
  30. 30.How far is the point (24, 7) from the origin (0, 0)? (a) 25 (b) 625 (c) 26 (d) 31
  31. 31.In which quadrant does the point (−3, −1) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  32. 32.What is the midpoint of the line joining (3, 8) and (7, 16)? (a) (12, 5) (b) (5, 12) (c) (10, 24) (d) (2, 4)
  33. 33.In which quadrant does the point (−5, −6) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  34. 34.What is the distance between the points (5, 8) and (17, 17)? (a) 16 (b) 21 (c) 225 (d) 15
  35. 35.In which quadrant does the point (−8, 8) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  36. 36.What is the distance between the points (9, 4) and (33, 11)? (a) 31 (b) 625 (c) 25 (d) 26
  37. 37.What is the distance between the points (1, 2) and (7, 10)? (a) 100 (b) 14 (c) 11 (d) 10
  38. 38.What is the distance between the points (9, 24) and (16, 0)? (a) 25 (b) 31 (c) 625 (d) 26
  39. 39.How far is the point (4, 3) from the origin (0, 0)? (a) 5 (b) 7 (c) 25 (d) 6
  40. 40.What is the distance between the points (1, 6) and (13, 11)? (a) 14 (b) 169 (c) 17 (d) 13

Answer key

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

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