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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 218 · 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 (5, 8) and (8, 4)? (a) 7 (b) 6 (c) 5 (d) 25
  2. 2.What is the distance between the points (1, 10) and (13, 1)? (a) 16 (b) 15 (c) 225 (d) 21
  3. 3.What is the midpoint of the line joining (4, 0) and (10, 8)? (a) (7, 4) (b) (14, 8) (c) (4, 7) (d) (3, 4)
  4. 4.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 21 (c) 28 (d) 20
  5. 5.In which quadrant does the point (5, 7) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  6. 6.What is the distance between the points (3, 5) and (7, 8)? (a) 5 (b) 25 (c) 6 (d) 7
  7. 7.In which quadrant does the point (6, −9) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  8. 8.In which quadrant does the point (8, −8) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  9. 9.What is the distance between the points (3, 6) and (15, 22)? (a) 400 (b) 28 (c) 20 (d) 21
  10. 10.What is the distance between the points (5, 5) and (20, 13)? (a) 289 (b) 23 (c) 17 (d) 18
  11. 11.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 20 (c) 28 (d) 400
  12. 12.In which quadrant does the point (2, −7) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  13. 13.In which quadrant does the point (9, 5) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  14. 14.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 15 (c) 225 (d) 21
  15. 15.In which quadrant does the point (2, 8) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  16. 16.What is the distance between the points (6, 6) and (9, 10)? (a) 5 (b) 25 (c) 6 (d) 7
  17. 17.What is the midpoint of the line joining (2, 8) and (14, 18)? (a) (13, 8) (b) (6, 5) (c) (16, 26) (d) (8, 13)
  18. 18.In which quadrant does the point (1, 5) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  19. 19.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 100 (c) 14 (d) 10
  20. 20.What is the distance between the points (2, 2) and (7, 14)? (a) 13 (b) 17 (c) 169 (d) 14
  21. 21.In which quadrant does the point (−9, −2) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  22. 22.What is the distance between the points (1, 7) and (16, 15)? (a) 289 (b) 18 (c) 23 (d) 17
  23. 23.In which quadrant does the point (1, 6) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  24. 24.What is the distance between the points (5, 19) and (10, 7)? (a) 17 (b) 13 (c) 169 (d) 14
  25. 25.What is the midpoint of the line joining (2, 6) and (14, 12)? (a) (16, 18) (b) (6, 3) (c) (9, 8) (d) (8, 9)
  26. 26.In which quadrant does the point (5, 4) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  27. 27.What is the distance between the points (7, 16) and (19, 0)? (a) 28 (b) 400 (c) 21 (d) 20
  28. 28.What is the midpoint of the line joining (1, 11) and (3, 1)? (a) (1, 5) (b) (2, 6) (c) (4, 12) (d) (6, 2)
  29. 29.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 17 (c) 13 (d) 169
  30. 30.What is the midpoint of the line joining (7, 0) and (9, 4)? (a) (1, 2) (b) (2, 8) (c) (16, 4) (d) (8, 2)
  31. 31.In which quadrant does the point (−1, 3) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  32. 32.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 14 (c) 11 (d) 10
  33. 33.What is the midpoint of the line joining (5, 6) and (17, 12)? (a) (9, 11) (b) (22, 18) (c) (11, 9) (d) (6, 3)
  34. 34.In which quadrant does the point (−5, 8) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  35. 35.What is the midpoint of the line joining (2, 9) and (12, 21)? (a) (15, 7) (b) (5, 6) (c) (14, 30) (d) (7, 15)
  36. 36.What is the distance between the points (7, 16) and (13, 8)? (a) 11 (b) 14 (c) 100 (d) 10
  37. 37.How far is the point (12, 9) from the origin (0, 0)? (a) 15 (b) 21 (c) 16 (d) 225
  38. 38.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 5 (c) 25 (d) 7
  39. 39.What is the midpoint of the line joining (9, 4) and (15, 12)? (a) (8, 12) (b) (3, 4) (c) (12, 8) (d) (24, 16)
  40. 40.What is the distance between the points (1, 9) and (4, 13)? (a) 25 (b) 5 (c) 7 (d) 6

Answer key

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

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