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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 747 · 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.In which quadrant does the point (5, 1) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  2. 2.What is the midpoint of the line joining (4, 7) and (16, 19)? (a) (20, 26) (b) (6, 6) (c) (10, 13) (d) (13, 10)
  3. 3.What is the distance between the points (3, 8) and (10, 32)? (a) 26 (b) 31 (c) 25 (d) 625
  4. 4.What is the distance between the points (9, 4) and (16, 28)? (a) 26 (b) 625 (c) 31 (d) 25
  5. 5.In which quadrant does the point (2, 2) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  6. 6.What is the midpoint of the line joining (2, 3) and (12, 9)? (a) (6, 7) (b) (5, 3) (c) (14, 12) (d) (7, 6)
  7. 7.In which quadrant does the point (4, −9) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  8. 8.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 17 (c) 289 (d) 23
  9. 9.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 7 (c) 25 (d) 5
  10. 10.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 100 (c) 11 (d) 10
  11. 11.What is the midpoint of the line joining (10, 6) and (14, 14)? (a) (24, 20) (b) (2, 4) (c) (12, 10) (d) (10, 12)
  12. 12.What is the midpoint of the line joining (1, 7) and (3, 9)? (a) (8, 2) (b) (2, 8) (c) (1, 1) (d) (4, 16)
  13. 13.In which quadrant does the point (1, 1) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  14. 14.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 169 (c) 14 (d) 13
  15. 15.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 25 (c) 5 (d) 7
  16. 16.What is the distance between the points (7, 4) and (11, 7)? (a) 5 (b) 25 (c) 6 (d) 7
  17. 17.What is the distance between the points (6, 6) and (9, 10)? (a) 7 (b) 6 (c) 25 (d) 5
  18. 18.In which quadrant does the point (9, 9) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  19. 19.What is the distance between the points (2, 0) and (9, 24)? (a) 31 (b) 625 (c) 26 (d) 25
  20. 20.What is the distance between the points (5, 4) and (9, 7)? (a) 25 (b) 5 (c) 6 (d) 7
  21. 21.What is the distance between the points (2, 0) and (10, 15)? (a) 17 (b) 18 (c) 289 (d) 23
  22. 22.What is the distance between the points (8, 5) and (12, 2)? (a) 7 (b) 5 (c) 6 (d) 25
  23. 23.What is the distance between the points (7, 18) and (23, 6)? (a) 400 (b) 21 (c) 20 (d) 28
  24. 24.In which quadrant does the point (−1, −3) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  25. 25.How far is the point (12, 5) from the origin (0, 0)? (a) 13 (b) 17 (c) 169 (d) 14
  26. 26.What is the distance between the points (0, 16) and (15, 8)? (a) 23 (b) 289 (c) 17 (d) 18
  27. 27.In which quadrant does the point (−5, −5) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  28. 28.In which quadrant does the point (−2, −5) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  29. 29.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 21 (c) 16 (d) 15
  30. 30.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 289 (c) 18 (d) 23
  31. 31.What is the midpoint of the line joining (7, 17) and (19, 5)? (a) (13, 11) (b) (6, 6) (c) (26, 22) (d) (11, 13)
  32. 32.In which quadrant does the point (4, −3) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  33. 33.What is the midpoint of the line joining (9, 10) and (19, 18)? (a) (5, 4) (b) (14, 14) (c) (28, 28) (d) (15, 14)
  34. 34.What is the distance between the points (6, 16) and (12, 8)? (a) 11 (b) 10 (c) 100 (d) 14
  35. 35.In which quadrant does the point (−2, −3) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  36. 36.What is the midpoint of the line joining (4, 10) and (8, 16)? (a) (2, 3) (b) (12, 26) (c) (13, 6) (d) (6, 13)
  37. 37.What is the distance between the points (8, 17) and (13, 5)? (a) 17 (b) 14 (c) 169 (d) 13
  38. 38.What is the distance between the points (9, 9) and (14, 21)? (a) 14 (b) 169 (c) 13 (d) 17
  39. 39.What is the distance between the points (0, 17) and (12, 1)? (a) 20 (b) 400 (c) 21 (d) 28
  40. 40.What is the midpoint of the line joining (6, 8) and (8, 4)? (a) (6, 7) (b) (14, 12) (c) (1, 2) (d) (7, 6)

Answer key

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

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