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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 190 · 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 (−7, −7) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  2. 2.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 26 (c) 25 (d) 31
  3. 3.What is the midpoint of the line joining (3, 6) and (13, 14)? (a) (16, 20) (b) (5, 4) (c) (8, 10) (d) (10, 8)
  4. 4.In which quadrant does the point (3, −5) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  5. 5.In which quadrant does the point (−2, 5) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  6. 6.What is the midpoint of the line joining (6, 4) and (14, 12)? (a) (8, 10) (b) (4, 4) (c) (20, 16) (d) (10, 8)
  7. 7.What is the midpoint of the line joining (2, 18) and (6, 8)? (a) (4, 13) (b) (13, 4) (c) (8, 26) (d) (2, 5)
  8. 8.What is the distance between the points (8, 18) and (13, 6)? (a) 169 (b) 17 (c) 13 (d) 14
  9. 9.What is the distance between the points (0, 4) and (7, 28)? (a) 25 (b) 31 (c) 26 (d) 625
  10. 10.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 5 (c) 6 (d) 25
  11. 11.In which quadrant does the point (−6, 9) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  12. 12.In which quadrant does the point (2, 3) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  13. 13.How far is the point (12, 9) from the origin (0, 0)? (a) 15 (b) 21 (c) 225 (d) 16
  14. 14.What is the distance between the points (7, 4) and (16, 16)? (a) 21 (b) 15 (c) 225 (d) 16
  15. 15.What is the midpoint of the line joining (7, 6) and (15, 10)? (a) (22, 16) (b) (8, 11) (c) (11, 8) (d) (4, 2)
  16. 16.What is the distance between the points (7, 7) and (10, 11)? (a) 25 (b) 5 (c) 6 (d) 7
  17. 17.What is the distance between the points (1, 5) and (8, 29)? (a) 31 (b) 625 (c) 26 (d) 25
  18. 18.How far is the point (5, 12) from the origin (0, 0)? (a) 13 (b) 14 (c) 169 (d) 17
  19. 19.What is the midpoint of the line joining (2, 12) and (4, 4)? (a) (8, 3) (b) (3, 8) (c) (6, 16) (d) (1, 4)
  20. 20.What is the midpoint of the line joining (9, 3) and (11, 5)? (a) (20, 8) (b) (1, 1) (c) (10, 4) (d) (4, 10)
  21. 21.What is the distance between the points (6, 8) and (10, 11)? (a) 7 (b) 5 (c) 6 (d) 25
  22. 22.What is the midpoint of the line joining (6, 14) and (8, 2)? (a) (8, 7) (b) (7, 8) (c) (14, 16) (d) (1, 6)
  23. 23.In which quadrant does the point (3, −3) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  24. 24.What is the distance between the points (8, 2) and (20, 11)? (a) 16 (b) 21 (c) 225 (d) 15
  25. 25.What is the distance between the points (0, 12) and (16, 0)? (a) 21 (b) 28 (c) 400 (d) 20
  26. 26.What is the distance between the points (0, 2) and (7, 26)? (a) 26 (b) 625 (c) 31 (d) 25
  27. 27.In which quadrant does the point (4, −2) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  28. 28.What is the distance between the points (0, 10) and (4, 7)? (a) 7 (b) 25 (c) 6 (d) 5
  29. 29.What is the midpoint of the line joining (4, 8) and (8, 16)? (a) (12, 6) (b) (12, 24) (c) (6, 12) (d) (2, 4)
  30. 30.What is the distance between the points (5, 9) and (8, 5)? (a) 25 (b) 7 (c) 5 (d) 6
  31. 31.What is the midpoint of the line joining (4, 7) and (12, 3)? (a) (5, 8) (b) (4, 2) (c) (16, 10) (d) (8, 5)
  32. 32.In which quadrant does the point (3, −2) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  33. 33.What is the distance between the points (0, 2) and (12, 18)? (a) 21 (b) 400 (c) 28 (d) 20
  34. 34.What is the distance between the points (4, 8) and (8, 11)? (a) 5 (b) 7 (c) 6 (d) 25
  35. 35.In which quadrant does the point (4, 8) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  36. 36.In which quadrant does the point (−4, −1) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  37. 37.How far is the point (16, 12) from the origin (0, 0)? (a) 400 (b) 28 (c) 21 (d) 20
  38. 38.What is the midpoint of the line joining (3, 1) and (5, 9)? (a) (1, 4) (b) (8, 10) (c) (4, 5) (d) (5, 4)
  39. 39.In which quadrant does the point (−2, 9) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  40. 40.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 13 (c) 169 (d) 14

Answer key

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

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