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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 181 · 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.How far is the point (12, 9) from the origin (0, 0)? (a) 16 (b) 21 (c) 225 (d) 15
  2. 2.In which quadrant does the point (8, −1) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  3. 3.In which quadrant does the point (2, 4) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  4. 4.What is the distance between the points (2, 8) and (10, 23)? (a) 17 (b) 289 (c) 23 (d) 18
  5. 5.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 14 (c) 169 (d) 13
  6. 6.What is the midpoint of the line joining (0, 9) and (8, 15)? (a) (8, 24) (b) (12, 4) (c) (4, 12) (d) (4, 3)
  7. 7.In which quadrant does the point (2, 9) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  8. 8.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 28 (c) 21 (d) 400
  9. 9.What is the distance between the points (1, 15) and (7, 7)? (a) 11 (b) 14 (c) 10 (d) 100
  10. 10.What is the midpoint of the line joining (0, 2) and (8, 4)? (a) (8, 6) (b) (4, 3) (c) (4, 1) (d) (3, 4)
  11. 11.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 13 (c) 17 (d) 169
  12. 12.What is the midpoint of the line joining (3, 4) and (7, 0)? (a) (10, 4) (b) (5, 2) (c) (2, 5) (d) (2, 2)
  13. 13.What is the distance between the points (9, 0) and (21, 9)? (a) 21 (b) 225 (c) 15 (d) 16
  14. 14.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 400 (c) 20 (d) 28
  15. 15.What is the midpoint of the line joining (6, 12) and (18, 2)? (a) (24, 14) (b) (6, 5) (c) (7, 12) (d) (12, 7)
  16. 16.In which quadrant does the point (−5, 6) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  17. 17.What is the distance between the points (6, 6) and (10, 9)? (a) 7 (b) 25 (c) 5 (d) 6
  18. 18.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 100 (c) 10 (d) 11
  19. 19.In which quadrant does the point (2, 2) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  20. 20.What is the distance between the points (0, 20) and (12, 4)? (a) 20 (b) 21 (c) 28 (d) 400
  21. 21.In which quadrant does the point (−5, 3) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  22. 22.In which quadrant does the point (6, 2) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  23. 23.What is the midpoint of the line joining (7, 2) and (19, 8)? (a) (13, 5) (b) (5, 13) (c) (6, 3) (d) (26, 10)
  24. 24.What is the midpoint of the line joining (5, 15) and (9, 5)? (a) (2, 5) (b) (7, 10) (c) (14, 20) (d) (10, 7)
  25. 25.What is the midpoint of the line joining (5, 0) and (9, 2)? (a) (2, 1) (b) (1, 7) (c) (7, 1) (d) (14, 2)
  26. 26.In which quadrant does the point (−4, 8) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  27. 27.In which quadrant does the point (5, −6) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  28. 28.What is the midpoint of the line joining (3, 6) and (11, 18)? (a) (12, 7) (b) (4, 6) (c) (7, 12) (d) (14, 24)
  29. 29.What is the distance between the points (6, 2) and (9, 6)? (a) 25 (b) 5 (c) 6 (d) 7
  30. 30.What is the distance between the points (2, 23) and (10, 8)? (a) 17 (b) 289 (c) 18 (d) 23
  31. 31.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 18 (c) 289 (d) 17
  32. 32.What is the midpoint of the line joining (10, 7) and (18, 17)? (a) (28, 24) (b) (4, 5) (c) (14, 12) (d) (12, 14)
  33. 33.What is the distance between the points (9, 13) and (12, 9)? (a) 7 (b) 25 (c) 5 (d) 6
  34. 34.In which quadrant does the point (7, −4) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  35. 35.What is the distance between the points (3, 7) and (6, 11)? (a) 6 (b) 5 (c) 25 (d) 7
  36. 36.What is the distance between the points (8, 11) and (14, 3)? (a) 14 (b) 100 (c) 10 (d) 11
  37. 37.How far is the point (24, 7) from the origin (0, 0)? (a) 26 (b) 31 (c) 25 (d) 625
  38. 38.In which quadrant does the point (5, 4) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  39. 39.What is the distance between the points (4, 1) and (8, 4)? (a) 7 (b) 25 (c) 6 (d) 5
  40. 40.In which quadrant does the point (4, −4) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant

Answer key

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

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