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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 470 · 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 (2, 9) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  2. 2.What is the midpoint of the line joining (10, 7) and (22, 3)? (a) (6, 2) (b) (32, 10) (c) (5, 16) (d) (16, 5)
  3. 3.What is the distance between the points (4, 2) and (16, 7)? (a) 14 (b) 13 (c) 169 (d) 17
  4. 4.What is the distance between the points (6, 9) and (18, 4)? (a) 13 (b) 169 (c) 17 (d) 14
  5. 5.In which quadrant does the point (−6, 7) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  6. 6.How far is the point (12, 16) from the origin (0, 0)? (a) 20 (b) 21 (c) 28 (d) 400
  7. 7.What is the distance between the points (8, 15) and (14, 7)? (a) 100 (b) 11 (c) 14 (d) 10
  8. 8.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 23 (c) 17 (d) 18
  9. 9.In which quadrant does the point (1, −1) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  10. 10.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 14 (c) 100 (d) 11
  11. 11.In which quadrant does the point (9, 8) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  12. 12.What is the distance between the points (2, 4) and (10, 10)? (a) 14 (b) 100 (c) 11 (d) 10
  13. 13.What is the distance between the points (1, 29) and (8, 5)? (a) 26 (b) 31 (c) 25 (d) 625
  14. 14.What is the midpoint of the line joining (7, 6) and (13, 18)? (a) (3, 6) (b) (10, 12) (c) (20, 24) (d) (12, 10)
  15. 15.In which quadrant does the point (2, 3) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  16. 16.In which quadrant does the point (6, −2) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  17. 17.In which quadrant does the point (−8, −9) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  18. 18.What is the midpoint of the line joining (9, 2) and (15, 12)? (a) (7, 12) (b) (24, 14) (c) (12, 7) (d) (3, 5)
  19. 19.What is the distance between the points (3, 6) and (19, 18)? (a) 28 (b) 20 (c) 21 (d) 400
  20. 20.In which quadrant does the point (7, −8) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  21. 21.What is the distance between the points (9, 5) and (15, 13)? (a) 10 (b) 14 (c) 11 (d) 100
  22. 22.What is the midpoint of the line joining (8, 1) and (12, 7)? (a) (2, 3) (b) (10, 4) (c) (20, 8) (d) (4, 10)
  23. 23.What is the midpoint of the line joining (0, 10) and (2, 20)? (a) (15, 1) (b) (1, 5) (c) (1, 15) (d) (2, 30)
  24. 24.What is the distance between the points (2, 5) and (11, 17)? (a) 21 (b) 16 (c) 15 (d) 225
  25. 25.What is the distance between the points (4, 5) and (16, 10)? (a) 169 (b) 17 (c) 13 (d) 14
  26. 26.What is the distance between the points (3, 17) and (15, 1)? (a) 20 (b) 21 (c) 400 (d) 28
  27. 27.In which quadrant does the point (5, 4) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  28. 28.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 400 (c) 21 (d) 20
  29. 29.In which quadrant does the point (8, 7) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  30. 30.What is the distance between the points (4, 10) and (10, 2)? (a) 100 (b) 10 (c) 14 (d) 11
  31. 31.In which quadrant does the point (3, 7) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  32. 32.What is the midpoint of the line joining (7, 18) and (11, 6)? (a) (9, 12) (b) (18, 24) (c) (2, 6) (d) (12, 9)
  33. 33.What is the distance between the points (3, 8) and (18, 0)? (a) 18 (b) 23 (c) 289 (d) 17
  34. 34.What is the midpoint of the line joining (7, 3) and (9, 7)? (a) (1, 2) (b) (16, 10) (c) (5, 8) (d) (8, 5)
  35. 35.What is the midpoint of the line joining (4, 20) and (12, 10)? (a) (15, 8) (b) (16, 30) (c) (8, 15) (d) (4, 5)
  36. 36.What is the distance between the points (6, 8) and (10, 5)? (a) 25 (b) 7 (c) 5 (d) 6
  37. 37.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 15 (c) 16 (d) 225
  38. 38.What is the distance between the points (7, 16) and (12, 4)? (a) 14 (b) 13 (c) 17 (d) 169
  39. 39.What is the midpoint of the line joining (4, 19) and (6, 7)? (a) (13, 5) (b) (5, 13) (c) (10, 26) (d) (1, 6)
  40. 40.What is the midpoint of the line joining (2, 15) and (10, 7)? (a) (4, 4) (b) (11, 6) (c) (12, 22) (d) (6, 11)

Answer key

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

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