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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 957 · 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 midpoint of the line joining (1, 20) and (11, 10)? (a) (5, 5) (b) (6, 15) (c) (12, 30) (d) (15, 6)
  2. 2.In which quadrant does the point (−9, 8) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  3. 3.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 25 (c) 625 (d) 26
  4. 4.What is the distance between the points (1, 2) and (6, 14)? (a) 13 (b) 169 (c) 14 (d) 17
  5. 5.What is the distance between the points (4, 11) and (28, 4)? (a) 26 (b) 625 (c) 25 (d) 31
  6. 6.What is the midpoint of the line joining (10, 5) and (22, 7)? (a) (32, 12) (b) (6, 1) (c) (6, 16) (d) (16, 6)
  7. 7.What is the distance between the points (5, 8) and (9, 11)? (a) 25 (b) 7 (c) 6 (d) 5
  8. 8.What is the distance between the points (0, 1) and (8, 16)? (a) 18 (b) 17 (c) 289 (d) 23
  9. 9.What is the distance between the points (3, 12) and (12, 0)? (a) 21 (b) 225 (c) 16 (d) 15
  10. 10.In which quadrant does the point (2, −5) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  11. 11.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 7 (c) 6 (d) 5
  12. 12.In which quadrant does the point (5, −7) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  13. 13.In which quadrant does the point (−8, −8) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  14. 14.In which quadrant does the point (−1, −7) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  15. 15.How far is the point (12, 16) from the origin (0, 0)? (a) 20 (b) 21 (c) 400 (d) 28
  16. 16.What is the distance between the points (8, 0) and (23, 8)? (a) 289 (b) 17 (c) 18 (d) 23
  17. 17.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 169 (c) 14 (d) 13
  18. 18.What is the distance between the points (5, 24) and (12, 0)? (a) 31 (b) 25 (c) 625 (d) 26
  19. 19.In which quadrant does the point (3, −9) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  20. 20.In which quadrant does the point (2, −8) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  21. 21.What is the midpoint of the line joining (6, 16) and (14, 10)? (a) (13, 10) (b) (20, 26) (c) (4, 3) (d) (10, 13)
  22. 22.In which quadrant does the point (6, 9) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  23. 23.What is the midpoint of the line joining (4, 9) and (6, 13)? (a) (11, 5) (b) (1, 2) (c) (10, 22) (d) (5, 11)
  24. 24.What is the distance between the points (8, 10) and (12, 7)? (a) 7 (b) 5 (c) 25 (d) 6
  25. 25.In which quadrant does the point (−7, 3) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  26. 26.In which quadrant does the point (8, 6) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  27. 27.In which quadrant does the point (6, −2) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  28. 28.What is the distance between the points (1, 20) and (6, 8)? (a) 169 (b) 17 (c) 14 (d) 13
  29. 29.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 13 (c) 14 (d) 169
  30. 30.In which quadrant does the point (1, −6) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  31. 31.What is the midpoint of the line joining (8, 9) and (10, 21)? (a) (1, 6) (b) (18, 30) (c) (9, 15) (d) (15, 9)
  32. 32.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 100 (c) 11 (d) 10
  33. 33.What is the distance between the points (8, 12) and (12, 9)? (a) 25 (b) 7 (c) 6 (d) 5
  34. 34.What is the midpoint of the line joining (4, 22) and (16, 10)? (a) (6, 6) (b) (10, 16) (c) (16, 10) (d) (20, 32)
  35. 35.What is the midpoint of the line joining (10, 14) and (20, 4)? (a) (30, 18) (b) (9, 15) (c) (15, 9) (d) (5, 5)
  36. 36.In which quadrant does the point (−2, 4) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  37. 37.What is the distance between the points (0, 15) and (12, 6)? (a) 15 (b) 21 (c) 225 (d) 16
  38. 38.What is the distance between the points (7, 3) and (14, 27)? (a) 31 (b) 625 (c) 26 (d) 25
  39. 39.In which quadrant does the point (7, 9) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  40. 40.What is the midpoint of the line joining (9, 9) and (17, 5)? (a) (4, 2) (b) (26, 14) (c) (13, 7) (d) (7, 13)

Answer key

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

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