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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 640 · 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 (5, −7) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  2. 2.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 25 (c) 6 (d) 5
  3. 3.In which quadrant does the point (7, 9) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  4. 4.What is the distance between the points (0, 24) and (7, 0)? (a) 26 (b) 625 (c) 31 (d) 25
  5. 5.How far is the point (24, 7) from the origin (0, 0)? (a) 25 (b) 26 (c) 625 (d) 31
  6. 6.In which quadrant does the point (−2, 4) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  7. 7.What is the midpoint of the line joining (9, 0) and (15, 8)? (a) (12, 4) (b) (3, 4) (c) (24, 8) (d) (4, 12)
  8. 8.In which quadrant does the point (7, 2) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  9. 9.In which quadrant does the point (8, −7) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  10. 10.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 400 (c) 28 (d) 20
  11. 11.What is the midpoint of the line joining (3, 2) and (15, 10)? (a) (6, 9) (b) (18, 12) (c) (9, 6) (d) (6, 4)
  12. 12.What is the distance between the points (5, 21) and (14, 9)? (a) 21 (b) 15 (c) 16 (d) 225
  13. 13.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 18 (c) 17 (d) 23
  14. 14.What is the midpoint of the line joining (2, 8) and (10, 2)? (a) (4, 3) (b) (5, 6) (c) (6, 5) (d) (12, 10)
  15. 15.In which quadrant does the point (−2, 7) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  16. 16.What is the midpoint of the line joining (4, 2) and (6, 4)? (a) (1, 1) (b) (10, 6) (c) (3, 5) (d) (5, 3)
  17. 17.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 20 (c) 21 (d) 400
  18. 18.What is the midpoint of the line joining (10, 16) and (18, 8)? (a) (12, 14) (b) (28, 24) (c) (14, 12) (d) (4, 4)
  19. 19.In which quadrant does the point (−7, 5) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  20. 20.What is the midpoint of the line joining (7, 1) and (13, 13)? (a) (20, 14) (b) (3, 6) (c) (10, 7) (d) (7, 10)
  21. 21.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 100 (c) 14 (d) 10
  22. 22.What is the midpoint of the line joining (3, 12) and (13, 4)? (a) (9, 8) (b) (8, 8) (c) (5, 4) (d) (16, 16)
  23. 23.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 13 (c) 17 (d) 169
  24. 24.In which quadrant does the point (−4, 8) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  25. 25.In which quadrant does the point (−3, −7) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  26. 26.In which quadrant does the point (1, −5) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  27. 27.What is the distance between the points (8, 11) and (12, 8)? (a) 5 (b) 25 (c) 7 (d) 6
  28. 28.What is the distance between the points (5, 6) and (10, 18)? (a) 13 (b) 169 (c) 17 (d) 14
  29. 29.What is the distance between the points (0, 14) and (9, 2)? (a) 21 (b) 225 (c) 15 (d) 16
  30. 30.In which quadrant does the point (4, −5) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  31. 31.What is the distance between the points (0, 9) and (3, 5)? (a) 6 (b) 5 (c) 7 (d) 25
  32. 32.What is the distance between the points (7, 10) and (13, 2)? (a) 10 (b) 14 (c) 100 (d) 11
  33. 33.In which quadrant does the point (−5, 2) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  34. 34.What is the distance between the points (0, 9) and (8, 24)? (a) 289 (b) 17 (c) 23 (d) 18
  35. 35.In which quadrant does the point (3, 7) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  36. 36.What is the distance between the points (0, 5) and (3, 1)? (a) 5 (b) 6 (c) 7 (d) 25
  37. 37.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 625 (c) 26 (d) 25
  38. 38.What is the midpoint of the line joining (5, 11) and (11, 3)? (a) (7, 8) (b) (3, 4) (c) (8, 7) (d) (16, 14)
  39. 39.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 5 (c) 25 (d) 7
  40. 40.What is the distance between the points (1, 8) and (7, 0)? (a) 100 (b) 14 (c) 10 (d) 11

Answer key

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

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