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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 562 · 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 (9, 15) and (18, 3)? (a) 16 (b) 225 (c) 15 (d) 21
  2. 2.What is the midpoint of the line joining (8, 3) and (12, 15)? (a) (2, 6) (b) (9, 10) (c) (20, 18) (d) (10, 9)
  3. 3.What is the distance between the points (1, 2) and (9, 8)? (a) 10 (b) 14 (c) 11 (d) 100
  4. 4.In which quadrant does the point (−6, −1) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  5. 5.What is the distance between the points (0, 7) and (9, 19)? (a) 21 (b) 16 (c) 225 (d) 15
  6. 6.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 100 (c) 11 (d) 10
  7. 7.What is the distance between the points (9, 3) and (17, 9)? (a) 14 (b) 10 (c) 11 (d) 100
  8. 8.What is the distance between the points (0, 7) and (12, 16)? (a) 15 (b) 225 (c) 21 (d) 16
  9. 9.What is the distance between the points (4, 0) and (28, 7)? (a) 31 (b) 26 (c) 625 (d) 25
  10. 10.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 17 (c) 14 (d) 13
  11. 11.What is the distance between the points (1, 9) and (7, 17)? (a) 11 (b) 10 (c) 100 (d) 14
  12. 12.What is the distance between the points (0, 12) and (8, 6)? (a) 100 (b) 11 (c) 10 (d) 14
  13. 13.What is the distance between the points (9, 2) and (21, 18)? (a) 28 (b) 21 (c) 20 (d) 400
  14. 14.What is the distance between the points (0, 5) and (8, 20)? (a) 18 (b) 23 (c) 289 (d) 17
  15. 15.In which quadrant does the point (4, −8) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  16. 16.In which quadrant does the point (2, 9) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  17. 17.In which quadrant does the point (5, 7) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  18. 18.In which quadrant does the point (−1, 4) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  19. 19.What is the distance between the points (5, 6) and (8, 10)? (a) 5 (b) 7 (c) 25 (d) 6
  20. 20.What is the distance between the points (7, 15) and (15, 9)? (a) 11 (b) 10 (c) 14 (d) 100
  21. 21.What is the midpoint of the line joining (4, 7) and (8, 13)? (a) (12, 20) (b) (6, 10) (c) (2, 3) (d) (10, 6)
  22. 22.What is the distance between the points (3, 7) and (15, 16)? (a) 21 (b) 225 (c) 16 (d) 15
  23. 23.What is the distance between the points (1, 0) and (9, 6)? (a) 14 (b) 11 (c) 10 (d) 100
  24. 24.What is the midpoint of the line joining (6, 16) and (12, 6)? (a) (18, 22) (b) (3, 5) (c) (9, 11) (d) (11, 9)
  25. 25.What is the midpoint of the line joining (3, 10) and (7, 8)? (a) (9, 5) (b) (2, 1) (c) (5, 9) (d) (10, 18)
  26. 26.In which quadrant does the point (−7, −7) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  27. 27.In which quadrant does the point (3, −3) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  28. 28.What is the midpoint of the line joining (8, 11) and (10, 5)? (a) (9, 8) (b) (8, 9) (c) (18, 16) (d) (1, 3)
  29. 29.What is the distance between the points (4, 7) and (28, 0)? (a) 625 (b) 31 (c) 25 (d) 26
  30. 30.What is the midpoint of the line joining (1, 10) and (7, 12)? (a) (4, 11) (b) (11, 4) (c) (8, 22) (d) (3, 1)
  31. 31.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 17 (c) 289 (d) 23
  32. 32.In which quadrant does the point (9, −9) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  33. 33.In which quadrant does the point (−3, −6) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  34. 34.What is the distance between the points (3, 9) and (19, 21)? (a) 21 (b) 28 (c) 20 (d) 400
  35. 35.In which quadrant does the point (8, 4) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  36. 36.In which quadrant does the point (−1, −4) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  37. 37.What is the distance between the points (2, 14) and (7, 2)? (a) 14 (b) 17 (c) 13 (d) 169
  38. 38.In which quadrant does the point (−8, −4) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  39. 39.In which quadrant does the point (−8, −1) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  40. 40.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 21 (c) 400 (d) 20

Answer key

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

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