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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 970 · 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, −3) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  2. 2.In which quadrant does the point (8, −1) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  3. 3.What is the midpoint of the line joining (9, 5) and (19, 15)? (a) (5, 5) (b) (28, 20) (c) (10, 14) (d) (14, 10)
  4. 4.In which quadrant does the point (−9, 2) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  5. 5.In which quadrant does the point (4, 3) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  6. 6.How far is the point (15, 8) from the origin (0, 0)? (a) 17 (b) 23 (c) 18 (d) 289
  7. 7.What is the distance between the points (5, 6) and (8, 2)? (a) 6 (b) 25 (c) 7 (d) 5
  8. 8.What is the distance between the points (4, 7) and (7, 11)? (a) 6 (b) 25 (c) 5 (d) 7
  9. 9.In which quadrant does the point (−2, −5) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  10. 10.In which quadrant does the point (−1, −9) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  11. 11.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 169 (c) 17 (d) 13
  12. 12.What is the midpoint of the line joining (9, 0) and (13, 4)? (a) (2, 2) (b) (2, 11) (c) (22, 4) (d) (11, 2)
  13. 13.In which quadrant does the point (−8, 3) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  14. 14.What is the midpoint of the line joining (2, 6) and (6, 2)? (a) (2, 2) (b) (8, 8) (c) (5, 4) (d) (4, 4)
  15. 15.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 225 (c) 16 (d) 15
  16. 16.In which quadrant does the point (7, 3) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  17. 17.What is the distance between the points (1, 0) and (10, 12)? (a) 16 (b) 15 (c) 225 (d) 21
  18. 18.What is the distance between the points (4, 17) and (12, 2)? (a) 17 (b) 289 (c) 23 (d) 18
  19. 19.What is the midpoint of the line joining (0, 4) and (10, 14)? (a) (9, 5) (b) (5, 5) (c) (10, 18) (d) (5, 9)
  20. 20.What is the distance between the points (2, 31) and (9, 7)? (a) 625 (b) 26 (c) 31 (d) 25
  21. 21.In which quadrant does the point (5, 4) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  22. 22.What is the distance between the points (8, 16) and (17, 4)? (a) 16 (b) 15 (c) 225 (d) 21
  23. 23.What is the distance between the points (4, 15) and (10, 7)? (a) 11 (b) 100 (c) 10 (d) 14
  24. 24.What is the distance between the points (4, 5) and (8, 8)? (a) 7 (b) 25 (c) 6 (d) 5
  25. 25.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 25 (c) 5 (d) 6
  26. 26.What is the midpoint of the line joining (3, 17) and (11, 7)? (a) (4, 5) (b) (12, 7) (c) (7, 12) (d) (14, 24)
  27. 27.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 14 (c) 100 (d) 11
  28. 28.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 21 (c) 20 (d) 400
  29. 29.In which quadrant does the point (−2, −7) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  30. 30.What is the midpoint of the line joining (4, 7) and (10, 9)? (a) (7, 8) (b) (3, 1) (c) (8, 7) (d) (14, 16)
  31. 31.What is the distance between the points (3, 15) and (11, 9)? (a) 100 (b) 10 (c) 11 (d) 14
  32. 32.How far is the point (4, 3) from the origin (0, 0)? (a) 5 (b) 6 (c) 7 (d) 25
  33. 33.In which quadrant does the point (6, −2) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  34. 34.What is the distance between the points (3, 10) and (7, 7)? (a) 5 (b) 7 (c) 6 (d) 25
  35. 35.What is the distance between the points (9, 1) and (12, 5)? (a) 6 (b) 5 (c) 25 (d) 7
  36. 36.What is the midpoint of the line joining (5, 15) and (7, 3)? (a) (12, 18) (b) (9, 6) (c) (6, 9) (d) (1, 6)
  37. 37.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 225 (c) 15 (d) 16
  38. 38.What is the distance between the points (4, 1) and (8, 4)? (a) 25 (b) 5 (c) 7 (d) 6
  39. 39.What is the distance between the points (6, 4) and (30, 11)? (a) 31 (b) 625 (c) 25 (d) 26
  40. 40.What is the distance between the points (9, 13) and (18, 1)? (a) 16 (b) 21 (c) 225 (d) 15

Answer key

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

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