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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 845 · 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, 25) and (9, 1)? (a) 625 (b) 26 (c) 31 (d) 25
  2. 2.What is the midpoint of the line joining (3, 13) and (15, 1)? (a) (9, 7) (b) (7, 9) (c) (6, 6) (d) (18, 14)
  3. 3.What is the distance between the points (6, 8) and (9, 12)? (a) 6 (b) 7 (c) 5 (d) 25
  4. 4.What is the midpoint of the line joining (3, 14) and (5, 4)? (a) (4, 9) (b) (8, 18) (c) (1, 5) (d) (9, 4)
  5. 5.In which quadrant does the point (1, 5) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  6. 6.What is the distance between the points (3, 0) and (11, 6)? (a) 11 (b) 10 (c) 14 (d) 100
  7. 7.What is the distance between the points (9, 11) and (13, 8)? (a) 5 (b) 25 (c) 7 (d) 6
  8. 8.What is the distance between the points (6, 9) and (22, 21)? (a) 400 (b) 20 (c) 21 (d) 28
  9. 9.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 25 (c) 6 (d) 5
  10. 10.What is the midpoint of the line joining (7, 14) and (13, 6)? (a) (20, 20) (b) (11, 10) (c) (3, 4) (d) (10, 10)
  11. 11.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 400 (c) 20 (d) 28
  12. 12.In which quadrant does the point (−7, −6) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  13. 13.What is the distance between the points (7, 11) and (19, 2)? (a) 21 (b) 225 (c) 16 (d) 15
  14. 14.In which quadrant does the point (8, 1) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  15. 15.What is the midpoint of the line joining (3, 2) and (13, 14)? (a) (16, 16) (b) (8, 8) (c) (5, 6) (d) (9, 8)
  16. 16.In which quadrant does the point (7, 1) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  17. 17.What is the distance between the points (9, 2) and (17, 17)? (a) 23 (b) 17 (c) 289 (d) 18
  18. 18.What is the distance between the points (1, 22) and (13, 6)? (a) 20 (b) 400 (c) 28 (d) 21
  19. 19.What is the distance between the points (5, 13) and (8, 9)? (a) 7 (b) 25 (c) 5 (d) 6
  20. 20.What is the distance between the points (2, 1) and (6, 4)? (a) 25 (b) 7 (c) 5 (d) 6
  21. 21.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 16 (c) 225 (d) 15
  22. 22.What is the midpoint of the line joining (10, 0) and (18, 6)? (a) (14, 3) (b) (3, 14) (c) (4, 3) (d) (28, 6)
  23. 23.In which quadrant does the point (5, 9) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  24. 24.In which quadrant does the point (6, 7) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  25. 25.What is the distance between the points (1, 7) and (10, 19)? (a) 225 (b) 21 (c) 15 (d) 16
  26. 26.What is the distance between the points (1, 0) and (13, 16)? (a) 400 (b) 21 (c) 28 (d) 20
  27. 27.In which quadrant does the point (−2, −6) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  28. 28.What is the midpoint of the line joining (0, 15) and (12, 5)? (a) (12, 20) (b) (6, 5) (c) (6, 10) (d) (10, 6)
  29. 29.What is the midpoint of the line joining (2, 10) and (6, 14)? (a) (2, 2) (b) (12, 4) (c) (8, 24) (d) (4, 12)
  30. 30.In which quadrant does the point (−1, −4) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  31. 31.What is the midpoint of the line joining (9, 21) and (17, 9)? (a) (13, 15) (b) (15, 13) (c) (26, 30) (d) (4, 6)
  32. 32.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 14 (c) 13 (d) 17
  33. 33.What is the midpoint of the line joining (2, 6) and (4, 18)? (a) (12, 3) (b) (1, 6) (c) (3, 12) (d) (6, 24)
  34. 34.In which quadrant does the point (−7, 9) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  35. 35.In which quadrant does the point (2, 2) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  36. 36.What is the distance between the points (1, 9) and (13, 18)? (a) 225 (b) 15 (c) 16 (d) 21
  37. 37.What is the distance between the points (1, 17) and (7, 9)? (a) 14 (b) 100 (c) 10 (d) 11
  38. 38.In which quadrant does the point (9, −5) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  39. 39.In which quadrant does the point (−7, 2) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  40. 40.In which quadrant does the point (5, 7) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant

Answer key

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

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