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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 908 · 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 (−2, 7) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  2. 2.What is the distance between the points (9, 24) and (21, 8)? (a) 400 (b) 21 (c) 28 (d) 20
  3. 3.In which quadrant does the point (−1, 4) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  4. 4.What is the midpoint of the line joining (6, 6) and (18, 18)? (a) (6, 6) (b) (24, 24) (c) (13, 12) (d) (12, 12)
  5. 5.In which quadrant does the point (1, −6) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  6. 6.In which quadrant does the point (−1, 3) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  7. 7.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 7 (c) 25 (d) 6
  8. 8.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 26 (c) 625 (d) 25
  9. 9.What is the midpoint of the line joining (4, 7) and (16, 17)? (a) (20, 24) (b) (12, 10) (c) (10, 12) (d) (6, 5)
  10. 10.What is the midpoint of the line joining (8, 15) and (18, 9)? (a) (5, 3) (b) (26, 24) (c) (13, 12) (d) (12, 13)
  11. 11.What is the midpoint of the line joining (7, 10) and (19, 20)? (a) (26, 30) (b) (6, 5) (c) (13, 15) (d) (15, 13)
  12. 12.In which quadrant does the point (3, −6) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  13. 13.What is the midpoint of the line joining (0, 7) and (12, 5)? (a) (7, 6) (b) (12, 12) (c) (6, 1) (d) (6, 6)
  14. 14.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 11 (c) 100 (d) 10
  15. 15.What is the midpoint of the line joining (2, 4) and (8, 10)? (a) (3, 3) (b) (7, 5) (c) (10, 14) (d) (5, 7)
  16. 16.What is the distance between the points (2, 2) and (10, 8)? (a) 100 (b) 10 (c) 11 (d) 14
  17. 17.What is the distance between the points (4, 11) and (10, 3)? (a) 100 (b) 11 (c) 14 (d) 10
  18. 18.What is the midpoint of the line joining (6, 18) and (8, 8)? (a) (7, 13) (b) (13, 7) (c) (14, 26) (d) (1, 5)
  19. 19.In which quadrant does the point (1, −2) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  20. 20.In which quadrant does the point (5, 1) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  21. 21.What is the midpoint of the line joining (1, 10) and (5, 16)? (a) (3, 13) (b) (6, 26) (c) (2, 3) (d) (13, 3)
  22. 22.What is the midpoint of the line joining (9, 7) and (11, 5)? (a) (1, 1) (b) (6, 10) (c) (20, 12) (d) (10, 6)
  23. 23.In which quadrant does the point (−5, −1) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  24. 24.In which quadrant does the point (−1, 5) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  25. 25.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 25 (c) 26 (d) 625
  26. 26.What is the distance between the points (1, 22) and (9, 7)? (a) 289 (b) 23 (c) 17 (d) 18
  27. 27.In which quadrant does the point (−7, 5) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  28. 28.In which quadrant does the point (−5, 1) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  29. 29.In which quadrant does the point (−1, 6) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  30. 30.What is the midpoint of the line joining (10, 22) and (18, 10)? (a) (28, 32) (b) (16, 14) (c) (4, 6) (d) (14, 16)
  31. 31.What is the distance between the points (7, 7) and (23, 19)? (a) 21 (b) 20 (c) 400 (d) 28
  32. 32.In which quadrant does the point (−2, −5) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  33. 33.What is the distance between the points (0, 8) and (9, 20)? (a) 16 (b) 225 (c) 21 (d) 15
  34. 34.In which quadrant does the point (−3, 8) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  35. 35.What is the midpoint of the line joining (0, 14) and (8, 2)? (a) (8, 16) (b) (4, 6) (c) (4, 8) (d) (8, 4)
  36. 36.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 23 (c) 18 (d) 17
  37. 37.What is the distance between the points (3, 9) and (19, 21)? (a) 28 (b) 21 (c) 20 (d) 400
  38. 38.In which quadrant does the point (−3, −2) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  39. 39.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 25 (c) 7 (d) 5
  40. 40.What is the midpoint of the line joining (5, 8) and (7, 10)? (a) (6, 9) (b) (9, 6) (c) (12, 18) (d) (1, 1)

Answer key

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

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