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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 635 · 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 (2, 14) and (17, 6)? (a) 17 (b) 23 (c) 18 (d) 289
  2. 2.What is the distance between the points (0, 8) and (3, 12)? (a) 25 (b) 6 (c) 7 (d) 5
  3. 3.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 5 (c) 6 (d) 25
  4. 4.In which quadrant does the point (1, −3) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  5. 5.What is the distance between the points (5, 20) and (10, 8)? (a) 17 (b) 13 (c) 14 (d) 169
  6. 6.What is the distance between the points (8, 2) and (23, 10)? (a) 289 (b) 17 (c) 18 (d) 23
  7. 7.What is the distance between the points (4, 7) and (16, 2)? (a) 169 (b) 14 (c) 13 (d) 17
  8. 8.What is the midpoint of the line joining (4, 7) and (14, 3)? (a) (18, 10) (b) (5, 2) (c) (9, 5) (d) (5, 9)
  9. 9.How far is the point (24, 7) from the origin (0, 0)? (a) 26 (b) 625 (c) 25 (d) 31
  10. 10.What is the distance between the points (0, 20) and (5, 8)? (a) 169 (b) 17 (c) 14 (d) 13
  11. 11.What is the midpoint of the line joining (5, 9) and (7, 11)? (a) (1, 1) (b) (12, 20) (c) (10, 6) (d) (6, 10)
  12. 12.What is the distance between the points (6, 6) and (11, 18)? (a) 169 (b) 13 (c) 14 (d) 17
  13. 13.What is the midpoint of the line joining (7, 9) and (13, 19)? (a) (3, 5) (b) (10, 14) (c) (20, 28) (d) (14, 10)
  14. 14.In which quadrant does the point (−1, 5) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  15. 15.What is the distance between the points (2, 9) and (8, 1)? (a) 14 (b) 11 (c) 100 (d) 10
  16. 16.What is the midpoint of the line joining (7, 10) and (17, 8)? (a) (24, 18) (b) (12, 9) (c) (9, 12) (d) (5, 1)
  17. 17.In which quadrant does the point (1, −2) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  18. 18.What is the distance between the points (8, 1) and (14, 9)? (a) 14 (b) 10 (c) 11 (d) 100
  19. 19.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 7 (c) 25 (d) 5
  20. 20.What is the midpoint of the line joining (9, 9) and (17, 11)? (a) (10, 13) (b) (26, 20) (c) (13, 10) (d) (4, 1)
  21. 21.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 400 (c) 20 (d) 28
  22. 22.What is the midpoint of the line joining (6, 18) and (16, 10)? (a) (14, 11) (b) (22, 28) (c) (11, 14) (d) (5, 4)
  23. 23.In which quadrant does the point (3, 9) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  24. 24.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 21 (c) 16 (d) 15
  25. 25.What is the distance between the points (5, 7) and (29, 0)? (a) 31 (b) 625 (c) 25 (d) 26
  26. 26.What is the distance between the points (1, 7) and (25, 14)? (a) 31 (b) 26 (c) 625 (d) 25
  27. 27.In which quadrant does the point (−2, −2) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  28. 28.In which quadrant does the point (−5, 1) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  29. 29.What is the distance between the points (4, 8) and (10, 16)? (a) 10 (b) 14 (c) 11 (d) 100
  30. 30.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 100 (c) 10 (d) 11
  31. 31.What is the midpoint of the line joining (10, 19) and (22, 7)? (a) (6, 6) (b) (13, 16) (c) (32, 26) (d) (16, 13)
  32. 32.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 23 (c) 18 (d) 17
  33. 33.In which quadrant does the point (2, 9) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  34. 34.In which quadrant does the point (−7, −1) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  35. 35.What is the distance between the points (0, 0) and (4, 3)? (a) 7 (b) 5 (c) 25 (d) 6
  36. 36.In which quadrant does the point (−5, 8) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  37. 37.What is the distance between the points (4, 3) and (11, 27)? (a) 625 (b) 26 (c) 25 (d) 31
  38. 38.What is the distance between the points (1, 21) and (6, 9)? (a) 169 (b) 14 (c) 13 (d) 17
  39. 39.In which quadrant does the point (2, 8) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  40. 40.What is the distance between the points (6, 8) and (30, 1)? (a) 31 (b) 26 (c) 25 (d) 625

Answer key

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

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