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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 132 · 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, 3) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  2. 2.In which quadrant does the point (−3, −8) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  3. 3.What is the midpoint of the line joining (7, 14) and (11, 8)? (a) (11, 9) (b) (9, 11) (c) (18, 22) (d) (2, 3)
  4. 4.What is the distance between the points (1, 19) and (6, 7)? (a) 14 (b) 17 (c) 169 (d) 13
  5. 5.What is the midpoint of the line joining (10, 18) and (14, 8)? (a) (24, 26) (b) (12, 13) (c) (2, 5) (d) (13, 12)
  6. 6.What is the distance between the points (8, 8) and (11, 4)? (a) 6 (b) 5 (c) 25 (d) 7
  7. 7.What is the midpoint of the line joining (1, 15) and (11, 5)? (a) (10, 6) (b) (5, 5) (c) (12, 20) (d) (6, 10)
  8. 8.What is the midpoint of the line joining (7, 13) and (17, 3)? (a) (8, 12) (b) (24, 16) (c) (5, 5) (d) (12, 8)
  9. 9.What is the distance between the points (1, 17) and (7, 9)? (a) 11 (b) 100 (c) 10 (d) 14
  10. 10.In which quadrant does the point (6, 5) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  11. 11.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 23 (c) 289 (d) 18
  12. 12.What is the midpoint of the line joining (9, 6) and (19, 4)? (a) (5, 1) (b) (5, 14) (c) (28, 10) (d) (14, 5)
  13. 13.What is the distance between the points (1, 5) and (4, 1)? (a) 25 (b) 7 (c) 6 (d) 5
  14. 14.What is the distance between the points (0, 4) and (6, 12)? (a) 100 (b) 14 (c) 11 (d) 10
  15. 15.What is the distance between the points (9, 3) and (25, 15)? (a) 400 (b) 21 (c) 20 (d) 28
  16. 16.What is the midpoint of the line joining (9, 2) and (15, 8)? (a) (3, 3) (b) (5, 12) (c) (24, 10) (d) (12, 5)
  17. 17.In which quadrant does the point (4, −4) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  18. 18.In which quadrant does the point (−8, 3) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  19. 19.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 5 (c) 25 (d) 7
  20. 20.What is the midpoint of the line joining (7, 5) and (13, 17)? (a) (20, 22) (b) (11, 10) (c) (3, 6) (d) (10, 11)
  21. 21.What is the distance between the points (2, 13) and (8, 5)? (a) 100 (b) 14 (c) 10 (d) 11
  22. 22.What is the distance between the points (8, 8) and (20, 17)? (a) 15 (b) 21 (c) 16 (d) 225
  23. 23.In which quadrant does the point (−6, 5) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  24. 24.What is the midpoint of the line joining (1, 10) and (13, 4)? (a) (8, 7) (b) (14, 14) (c) (7, 7) (d) (6, 3)
  25. 25.What is the midpoint of the line joining (8, 3) and (10, 11)? (a) (18, 14) (b) (7, 9) (c) (9, 7) (d) (1, 4)
  26. 26.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 16 (c) 15 (d) 21
  27. 27.What is the distance between the points (2, 7) and (10, 13)? (a) 14 (b) 11 (c) 100 (d) 10
  28. 28.What is the distance between the points (5, 4) and (10, 16)? (a) 14 (b) 13 (c) 169 (d) 17
  29. 29.What is the distance between the points (2, 2) and (6, 5)? (a) 25 (b) 7 (c) 6 (d) 5
  30. 30.In which quadrant does the point (−5, −1) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  31. 31.What is the distance between the points (3, 12) and (6, 8)? (a) 7 (b) 6 (c) 25 (d) 5
  32. 32.In which quadrant does the point (6, 1) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  33. 33.What is the distance between the points (9, 2) and (12, 6)? (a) 25 (b) 6 (c) 7 (d) 5
  34. 34.What is the distance between the points (4, 3) and (9, 15)? (a) 13 (b) 169 (c) 14 (d) 17
  35. 35.What is the midpoint of the line joining (1, 10) and (3, 18)? (a) (2, 14) (b) (1, 4) (c) (14, 2) (d) (4, 28)
  36. 36.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 26 (c) 31 (d) 25
  37. 37.What is the distance between the points (4, 2) and (12, 8)? (a) 100 (b) 11 (c) 14 (d) 10
  38. 38.What is the midpoint of the line joining (10, 12) and (18, 2)? (a) (14, 7) (b) (7, 14) (c) (28, 14) (d) (4, 5)
  39. 39.What is the midpoint of the line joining (2, 6) and (6, 10)? (a) (4, 8) (b) (2, 2) (c) (8, 16) (d) (8, 4)
  40. 40.What is the midpoint of the line joining (8, 11) and (12, 5)? (a) (8, 10) (b) (2, 3) (c) (20, 16) (d) (10, 8)

Answer key

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

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