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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 692 · 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 distance between the points (2, 8) and (5, 12)? (a) 7 (b) 6 (c) 25 (d) 5
  2. 2.What is the distance between the points (4, 27) and (11, 3)? (a) 625 (b) 26 (c) 31 (d) 25
  3. 3.What is the midpoint of the line joining (5, 12) and (11, 6)? (a) (16, 18) (b) (9, 8) (c) (8, 9) (d) (3, 3)
  4. 4.What is the midpoint of the line joining (0, 22) and (2, 10)? (a) (16, 1) (b) (2, 32) (c) (1, 6) (d) (1, 16)
  5. 5.In which quadrant does the point (1, −8) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  6. 6.What is the distance between the points (6, 3) and (14, 9)? (a) 10 (b) 11 (c) 100 (d) 14
  7. 7.What is the distance between the points (8, 5) and (24, 17)? (a) 400 (b) 28 (c) 21 (d) 20
  8. 8.In which quadrant does the point (−5, 5) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  9. 9.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 6 (c) 25 (d) 7
  10. 10.How far is the point (15, 8) from the origin (0, 0)? (a) 17 (b) 23 (c) 18 (d) 289
  11. 11.What is the distance between the points (5, 9) and (9, 6)? (a) 25 (b) 7 (c) 6 (d) 5
  12. 12.In which quadrant does the point (7, −4) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  13. 13.What is the distance between the points (3, 6) and (7, 9)? (a) 6 (b) 7 (c) 5 (d) 25
  14. 14.What is the distance between the points (2, 15) and (11, 3)? (a) 225 (b) 16 (c) 21 (d) 15
  15. 15.What is the distance between the points (1, 13) and (10, 1)? (a) 15 (b) 16 (c) 21 (d) 225
  16. 16.In which quadrant does the point (6, 4) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  17. 17.In which quadrant does the point (−7, 2) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  18. 18.What is the distance between the points (0, 10) and (6, 2)? (a) 11 (b) 10 (c) 100 (d) 14
  19. 19.What is the midpoint of the line joining (1, 6) and (5, 0)? (a) (3, 3) (b) (6, 6) (c) (2, 3) (d) (4, 3)
  20. 20.In which quadrant does the point (−2, −3) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  21. 21.In which quadrant does the point (9, −6) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  22. 22.What is the distance between the points (4, 9) and (16, 0)? (a) 16 (b) 21 (c) 225 (d) 15
  23. 23.What is the midpoint of the line joining (4, 19) and (16, 9)? (a) (14, 10) (b) (6, 5) (c) (10, 14) (d) (20, 28)
  24. 24.What is the midpoint of the line joining (6, 13) and (18, 5)? (a) (12, 9) (b) (9, 12) (c) (24, 18) (d) (6, 4)
  25. 25.In which quadrant does the point (2, 6) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  26. 26.What is the midpoint of the line joining (1, 10) and (5, 6)? (a) (6, 16) (b) (2, 2) (c) (3, 8) (d) (8, 3)
  27. 27.In which quadrant does the point (9, −3) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  28. 28.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 15 (c) 21 (d) 225
  29. 29.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 20 (c) 21 (d) 400
  30. 30.What is the distance between the points (6, 8) and (18, 3)? (a) 13 (b) 17 (c) 14 (d) 169
  31. 31.What is the distance between the points (4, 25) and (11, 1)? (a) 26 (b) 625 (c) 25 (d) 31
  32. 32.What is the midpoint of the line joining (3, 21) and (13, 9)? (a) (16, 30) (b) (8, 15) (c) (15, 8) (d) (5, 6)
  33. 33.In which quadrant does the point (−9, 6) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  34. 34.What is the midpoint of the line joining (2, 11) and (6, 1)? (a) (6, 4) (b) (2, 5) (c) (4, 6) (d) (8, 12)
  35. 35.What is the distance between the points (4, 2) and (8, 5)? (a) 7 (b) 5 (c) 25 (d) 6
  36. 36.In which quadrant does the point (−2, 3) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  37. 37.What is the distance between the points (7, 3) and (19, 8)? (a) 14 (b) 169 (c) 13 (d) 17
  38. 38.In which quadrant does the point (−8, −6) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  39. 39.In which quadrant does the point (−7, 4) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  40. 40.How far is the point (24, 7) from the origin (0, 0)? (a) 26 (b) 625 (c) 25 (d) 31

Answer key

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

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