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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 336 · 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, 1) and (9, 25)? (a) 31 (b) 26 (c) 625 (d) 25
  2. 2.What is the midpoint of the line joining (0, 2) and (10, 4)? (a) (10, 6) (b) (5, 1) (c) (3, 5) (d) (5, 3)
  3. 3.What is the distance between the points (4, 5) and (12, 11)? (a) 100 (b) 10 (c) 11 (d) 14
  4. 4.What is the midpoint of the line joining (4, 10) and (14, 6)? (a) (5, 2) (b) (8, 9) (c) (9, 8) (d) (18, 16)
  5. 5.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 23 (c) 17 (d) 18
  6. 6.What is the distance between the points (2, 8) and (6, 5)? (a) 7 (b) 25 (c) 6 (d) 5
  7. 7.What is the distance between the points (2, 7) and (26, 0)? (a) 625 (b) 26 (c) 25 (d) 31
  8. 8.What is the distance between the points (7, 11) and (22, 3)? (a) 289 (b) 18 (c) 17 (d) 23
  9. 9.In which quadrant does the point (8, 4) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  10. 10.What is the distance between the points (8, 5) and (20, 10)? (a) 169 (b) 17 (c) 14 (d) 13
  11. 11.What is the midpoint of the line joining (0, 13) and (10, 7)? (a) (10, 5) (b) (5, 3) (c) (5, 10) (d) (10, 20)
  12. 12.What is the midpoint of the line joining (2, 9) and (8, 7)? (a) (5, 8) (b) (3, 1) (c) (8, 5) (d) (10, 16)
  13. 13.In which quadrant does the point (−2, 3) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  14. 14.In which quadrant does the point (4, 2) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  15. 15.In which quadrant does the point (−8, 5) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  16. 16.In which quadrant does the point (5, 5) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  17. 17.What is the distance between the points (9, 4) and (21, 13)? (a) 225 (b) 16 (c) 15 (d) 21
  18. 18.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 16 (c) 15 (d) 21
  19. 19.What is the distance between the points (3, 4) and (7, 1)? (a) 25 (b) 7 (c) 6 (d) 5
  20. 20.In which quadrant does the point (−6, −1) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  21. 21.In which quadrant does the point (−6, −3) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  22. 22.In which quadrant does the point (−2, 2) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  23. 23.What is the distance between the points (4, 12) and (13, 0)? (a) 225 (b) 21 (c) 15 (d) 16
  24. 24.In which quadrant does the point (2, −5) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  25. 25.What is the midpoint of the line joining (8, 12) and (20, 0)? (a) (6, 14) (b) (28, 12) (c) (14, 6) (d) (6, 6)
  26. 26.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 13 (c) 169 (d) 17
  27. 27.What is the midpoint of the line joining (5, 8) and (15, 16)? (a) (20, 24) (b) (5, 4) (c) (10, 12) (d) (12, 10)
  28. 28.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 400 (c) 21 (d) 28
  29. 29.What is the distance between the points (6, 5) and (12, 13)? (a) 14 (b) 100 (c) 11 (d) 10
  30. 30.In which quadrant does the point (−5, −9) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  31. 31.In which quadrant does the point (2, −9) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  32. 32.What is the midpoint of the line joining (10, 4) and (12, 6)? (a) (11, 5) (b) (1, 1) (c) (5, 11) (d) (22, 10)
  33. 33.What is the midpoint of the line joining (3, 1) and (13, 7)? (a) (5, 3) (b) (16, 8) (c) (4, 8) (d) (8, 4)
  34. 34.In which quadrant does the point (4, −1) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  35. 35.What is the distance between the points (8, 1) and (14, 9)? (a) 100 (b) 14 (c) 11 (d) 10
  36. 36.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 10 (c) 100 (d) 14
  37. 37.What is the midpoint of the line joining (5, 10) and (9, 0)? (a) (7, 5) (b) (5, 7) (c) (14, 10) (d) (2, 5)
  38. 38.What is the distance between the points (9, 20) and (17, 5)? (a) 23 (b) 289 (c) 18 (d) 17
  39. 39.How far is the point (12, 16) from the origin (0, 0)? (a) 20 (b) 400 (c) 21 (d) 28
  40. 40.In which quadrant does the point (−2, −6) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant

Answer key

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

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