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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 601 · 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 (−9, 8) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  2. 2.What is the distance between the points (0, 4) and (8, 10)? (a) 100 (b) 11 (c) 10 (d) 14
  3. 3.What is the midpoint of the line joining (0, 5) and (8, 3)? (a) (8, 8) (b) (5, 4) (c) (4, 1) (d) (4, 4)
  4. 4.What is the distance between the points (0, 17) and (8, 2)? (a) 23 (b) 17 (c) 18 (d) 289
  5. 5.In which quadrant does the point (3, 8) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  6. 6.What is the midpoint of the line joining (5, 16) and (13, 6)? (a) (4, 5) (b) (18, 22) (c) (11, 9) (d) (9, 11)
  7. 7.What is the distance between the points (2, 10) and (10, 4)? (a) 10 (b) 100 (c) 14 (d) 11
  8. 8.How far is the point (12, 9) from the origin (0, 0)? (a) 15 (b) 21 (c) 16 (d) 225
  9. 9.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 7 (c) 5 (d) 6
  10. 10.In which quadrant does the point (5, −9) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  11. 11.What is the distance between the points (5, 0) and (8, 4)? (a) 25 (b) 5 (c) 7 (d) 6
  12. 12.In which quadrant does the point (2, 1) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  13. 13.What is the distance between the points (0, 8) and (8, 2)? (a) 10 (b) 11 (c) 100 (d) 14
  14. 14.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 20 (c) 400 (d) 28
  15. 15.What is the midpoint of the line joining (7, 13) and (19, 7)? (a) (26, 20) (b) (13, 10) (c) (10, 13) (d) (6, 3)
  16. 16.What is the midpoint of the line joining (0, 9) and (6, 3)? (a) (3, 3) (b) (6, 3) (c) (6, 12) (d) (3, 6)
  17. 17.What is the distance between the points (6, 11) and (10, 8)? (a) 5 (b) 7 (c) 6 (d) 25
  18. 18.How far is the point (24, 7) from the origin (0, 0)? (a) 25 (b) 31 (c) 26 (d) 625
  19. 19.What is the distance between the points (4, 9) and (16, 0)? (a) 225 (b) 21 (c) 15 (d) 16
  20. 20.What is the distance between the points (3, 3) and (7, 0)? (a) 5 (b) 7 (c) 6 (d) 25
  21. 21.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 17 (c) 13 (d) 169
  22. 22.What is the midpoint of the line joining (8, 5) and (16, 13)? (a) (4, 4) (b) (24, 18) (c) (12, 9) (d) (9, 12)
  23. 23.What is the midpoint of the line joining (8, 17) and (10, 9)? (a) (9, 13) (b) (1, 4) (c) (13, 9) (d) (18, 26)
  24. 24.In which quadrant does the point (9, 1) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  25. 25.What is the distance between the points (2, 5) and (6, 8)? (a) 5 (b) 25 (c) 7 (d) 6
  26. 26.What is the midpoint of the line joining (5, 16) and (7, 4)? (a) (6, 10) (b) (1, 6) (c) (10, 6) (d) (12, 20)
  27. 27.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 26 (c) 625 (d) 25
  28. 28.What is the midpoint of the line joining (2, 8) and (6, 4)? (a) (4, 6) (b) (6, 4) (c) (8, 12) (d) (2, 2)
  29. 29.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 20 (c) 21 (d) 400
  30. 30.What is the distance between the points (9, 20) and (18, 8)? (a) 15 (b) 21 (c) 16 (d) 225
  31. 31.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 6 (c) 5 (d) 7
  32. 32.What is the distance between the points (6, 2) and (11, 14)? (a) 169 (b) 14 (c) 13 (d) 17
  33. 33.What is the distance between the points (8, 10) and (20, 1)? (a) 225 (b) 21 (c) 15 (d) 16
  34. 34.What is the distance between the points (1, 21) and (10, 9)? (a) 16 (b) 15 (c) 225 (d) 21
  35. 35.What is the distance between the points (9, 2) and (21, 18)? (a) 28 (b) 400 (c) 20 (d) 21
  36. 36.In which quadrant does the point (8, −8) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  37. 37.What is the distance between the points (0, 7) and (12, 23)? (a) 21 (b) 20 (c) 400 (d) 28
  38. 38.In which quadrant does the point (−6, 8) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  39. 39.In which quadrant does the point (1, 9) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  40. 40.How far is the point (12, 5) from the origin (0, 0)? (a) 13 (b) 14 (c) 169 (d) 17

Answer key

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

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