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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 203 · 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 (8, 4) and (12, 1)? (a) 6 (b) 5 (c) 25 (d) 7
  2. 2.What is the midpoint of the line joining (9, 2) and (19, 8)? (a) (5, 14) (b) (28, 10) (c) (5, 3) (d) (14, 5)
  3. 3.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 6 (c) 5 (d) 7
  4. 4.What is the distance between the points (9, 1) and (14, 13)? (a) 169 (b) 17 (c) 14 (d) 13
  5. 5.In which quadrant does the point (−1, −1) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  6. 6.What is the distance between the points (0, 19) and (5, 7)? (a) 13 (b) 14 (c) 169 (d) 17
  7. 7.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 289 (c) 17 (d) 18
  8. 8.In which quadrant does the point (1, 1) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  9. 9.What is the distance between the points (4, 8) and (12, 14)? (a) 100 (b) 14 (c) 10 (d) 11
  10. 10.In which quadrant does the point (−8, 8) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  11. 11.What is the distance between the points (9, 24) and (21, 8)? (a) 28 (b) 400 (c) 20 (d) 21
  12. 12.What is the midpoint of the line joining (0, 2) and (4, 12)? (a) (7, 2) (b) (4, 14) (c) (2, 5) (d) (2, 7)
  13. 13.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 100 (c) 11 (d) 10
  14. 14.What is the distance between the points (7, 1) and (23, 13)? (a) 21 (b) 400 (c) 28 (d) 20
  15. 15.In which quadrant does the point (1, 7) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  16. 16.How far is the point (12, 9) from the origin (0, 0)? (a) 15 (b) 21 (c) 225 (d) 16
  17. 17.What is the midpoint of the line joining (0, 8) and (2, 4)? (a) (2, 12) (b) (1, 2) (c) (1, 6) (d) (6, 1)
  18. 18.What is the distance between the points (7, 3) and (16, 15)? (a) 225 (b) 16 (c) 21 (d) 15
  19. 19.In which quadrant does the point (−8, −9) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  20. 20.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 13 (c) 17 (d) 14
  21. 21.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 11 (c) 10 (d) 14
  22. 22.What is the midpoint of the line joining (9, 9) and (19, 21)? (a) (5, 6) (b) (14, 15) (c) (15, 14) (d) (28, 30)
  23. 23.In which quadrant does the point (4, −8) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  24. 24.What is the distance between the points (5, 1) and (8, 5)? (a) 25 (b) 7 (c) 5 (d) 6
  25. 25.What is the midpoint of the line joining (2, 9) and (14, 11)? (a) (10, 8) (b) (8, 10) (c) (16, 20) (d) (6, 1)
  26. 26.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 20 (c) 400 (d) 21
  27. 27.In which quadrant does the point (−1, 7) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  28. 28.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 25 (c) 26 (d) 31
  29. 29.What is the midpoint of the line joining (7, 4) and (17, 12)? (a) (24, 16) (b) (5, 4) (c) (12, 8) (d) (8, 12)
  30. 30.What is the distance between the points (2, 16) and (14, 0)? (a) 400 (b) 20 (c) 28 (d) 21
  31. 31.What is the midpoint of the line joining (7, 5) and (19, 17)? (a) (6, 6) (b) (13, 11) (c) (11, 13) (d) (26, 22)
  32. 32.What is the midpoint of the line joining (7, 9) and (19, 3)? (a) (6, 3) (b) (6, 13) (c) (13, 6) (d) (26, 12)
  33. 33.What is the midpoint of the line joining (0, 9) and (6, 21)? (a) (3, 15) (b) (3, 6) (c) (6, 30) (d) (15, 3)
  34. 34.In which quadrant does the point (5, 6) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  35. 35.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 18 (c) 17 (d) 289
  36. 36.In which quadrant does the point (8, 7) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  37. 37.In which quadrant does the point (−4, −3) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  38. 38.In which quadrant does the point (7, −9) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  39. 39.What is the distance between the points (7, 5) and (15, 11)? (a) 10 (b) 14 (c) 11 (d) 100
  40. 40.In which quadrant does the point (9, 7) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant

Answer key

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

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