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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 794 · 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 (−6, 1) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  2. 2.In which quadrant does the point (−4, 1) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  3. 3.What is the midpoint of the line joining (2, 7) and (4, 3)? (a) (5, 3) (b) (3, 5) (c) (6, 10) (d) (1, 2)
  4. 4.What is the distance between the points (8, 8) and (12, 5)? (a) 7 (b) 25 (c) 6 (d) 5
  5. 5.What is the midpoint of the line joining (2, 3) and (14, 7)? (a) (5, 8) (b) (6, 2) (c) (8, 5) (d) (16, 10)
  6. 6.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 17 (c) 18 (d) 23
  7. 7.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 100 (c) 10 (d) 11
  8. 8.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 14 (c) 13 (d) 169
  9. 9.How far is the point (4, 3) from the origin (0, 0)? (a) 5 (b) 6 (c) 7 (d) 25
  10. 10.In which quadrant does the point (1, 4) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  11. 11.In which quadrant does the point (−8, −1) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  12. 12.What is the midpoint of the line joining (10, 10) and (12, 16)? (a) (13, 11) (b) (22, 26) (c) (11, 13) (d) (1, 3)
  13. 13.What is the midpoint of the line joining (0, 1) and (10, 3)? (a) (5, 1) (b) (10, 4) (c) (2, 5) (d) (5, 2)
  14. 14.In which quadrant does the point (7, 4) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  15. 15.What is the distance between the points (7, 4) and (12, 16)? (a) 169 (b) 17 (c) 14 (d) 13
  16. 16.In which quadrant does the point (−1, −4) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  17. 17.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 10 (c) 14 (d) 100
  18. 18.What is the distance between the points (3, 0) and (10, 24)? (a) 625 (b) 31 (c) 26 (d) 25
  19. 19.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 21 (c) 15 (d) 16
  20. 20.What is the distance between the points (1, 0) and (8, 24)? (a) 26 (b) 625 (c) 31 (d) 25
  21. 21.What is the distance between the points (5, 25) and (12, 1)? (a) 26 (b) 25 (c) 31 (d) 625
  22. 22.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 5 (c) 25 (d) 6
  23. 23.What is the midpoint of the line joining (9, 7) and (21, 5)? (a) (30, 12) (b) (6, 1) (c) (15, 6) (d) (6, 15)
  24. 24.How far is the point (12, 16) from the origin (0, 0)? (a) 20 (b) 28 (c) 400 (d) 21
  25. 25.What is the midpoint of the line joining (8, 7) and (18, 19)? (a) (26, 26) (b) (14, 13) (c) (13, 13) (d) (5, 6)
  26. 26.What is the distance between the points (4, 7) and (28, 14)? (a) 26 (b) 625 (c) 25 (d) 31
  27. 27.What is the midpoint of the line joining (6, 2) and (14, 0)? (a) (20, 2) (b) (1, 10) (c) (10, 1) (d) (4, 1)
  28. 28.What is the distance between the points (5, 5) and (20, 13)? (a) 23 (b) 289 (c) 18 (d) 17
  29. 29.What is the distance between the points (3, 10) and (18, 2)? (a) 17 (b) 18 (c) 289 (d) 23
  30. 30.In which quadrant does the point (−6, 8) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  31. 31.In which quadrant does the point (6, 1) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  32. 32.What is the midpoint of the line joining (6, 10) and (8, 14)? (a) (12, 7) (b) (7, 12) (c) (1, 2) (d) (14, 24)
  33. 33.In which quadrant does the point (−7, 6) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  34. 34.In which quadrant does the point (−2, 4) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  35. 35.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 17 (c) 18 (d) 23
  36. 36.What is the distance between the points (4, 12) and (16, 3)? (a) 15 (b) 16 (c) 225 (d) 21
  37. 37.What is the distance between the points (3, 16) and (9, 8)? (a) 10 (b) 14 (c) 100 (d) 11
  38. 38.What is the distance between the points (0, 10) and (12, 1)? (a) 15 (b) 225 (c) 16 (d) 21
  39. 39.What is the midpoint of the line joining (9, 9) and (17, 11)? (a) (13, 10) (b) (4, 1) (c) (26, 20) (d) (10, 13)
  40. 40.What is the midpoint of the line joining (5, 2) and (7, 6)? (a) (1, 2) (b) (6, 4) (c) (4, 6) (d) (12, 8)

Answer key

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

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