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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 295 · 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, 9) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  2. 2.In which quadrant does the point (−9, 9) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  3. 3.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 25 (c) 6 (d) 5
  4. 4.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 21 (c) 400 (d) 20
  5. 5.In which quadrant does the point (−3, 6) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  6. 6.In which quadrant does the point (−3, −3) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  7. 7.In which quadrant does the point (4, −5) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  8. 8.How far is the point (12, 9) from the origin (0, 0)? (a) 15 (b) 225 (c) 16 (d) 21
  9. 9.What is the distance between the points (2, 2) and (14, 18)? (a) 20 (b) 28 (c) 21 (d) 400
  10. 10.In which quadrant does the point (8, −2) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  11. 11.In which quadrant does the point (−8, −5) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  12. 12.What is the distance between the points (8, 7) and (32, 0)? (a) 31 (b) 25 (c) 625 (d) 26
  13. 13.What is the distance between the points (7, 13) and (10, 9)? (a) 25 (b) 7 (c) 6 (d) 5
  14. 14.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 17 (c) 289 (d) 23
  15. 15.What is the distance between the points (5, 7) and (11, 15)? (a) 14 (b) 11 (c) 10 (d) 100
  16. 16.What is the midpoint of the line joining (9, 10) and (17, 14)? (a) (26, 24) (b) (12, 13) (c) (13, 12) (d) (4, 2)
  17. 17.What is the midpoint of the line joining (1, 0) and (9, 10)? (a) (10, 10) (b) (6, 5) (c) (4, 5) (d) (5, 5)
  18. 18.What is the midpoint of the line joining (6, 5) and (18, 15)? (a) (10, 12) (b) (6, 5) (c) (24, 20) (d) (12, 10)
  19. 19.What is the distance between the points (7, 19) and (12, 7)? (a) 14 (b) 13 (c) 169 (d) 17
  20. 20.In which quadrant does the point (2, 4) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  21. 21.What is the distance between the points (0, 15) and (8, 9)? (a) 100 (b) 10 (c) 11 (d) 14
  22. 22.In which quadrant does the point (−2, −1) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  23. 23.What is the distance between the points (3, 2) and (15, 7)? (a) 169 (b) 13 (c) 14 (d) 17
  24. 24.What is the distance between the points (4, 2) and (16, 18)? (a) 400 (b) 20 (c) 28 (d) 21
  25. 25.What is the midpoint of the line joining (8, 4) and (12, 8)? (a) (6, 10) (b) (2, 2) (c) (20, 12) (d) (10, 6)
  26. 26.In which quadrant does the point (−1, 1) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  27. 27.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 31 (c) 25 (d) 26
  28. 28.What is the distance between the points (0, 1) and (6, 9)? (a) 10 (b) 100 (c) 14 (d) 11
  29. 29.In which quadrant does the point (5, −4) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  30. 30.In which quadrant does the point (−7, 4) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  31. 31.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 400 (c) 20 (d) 21
  32. 32.What is the distance between the points (1, 3) and (25, 10)? (a) 31 (b) 25 (c) 625 (d) 26
  33. 33.What is the midpoint of the line joining (6, 19) and (12, 7)? (a) (13, 9) (b) (9, 13) (c) (18, 26) (d) (3, 6)
  34. 34.What is the distance between the points (9, 17) and (15, 9)? (a) 10 (b) 11 (c) 14 (d) 100
  35. 35.What is the midpoint of the line joining (10, 15) and (16, 9)? (a) (13, 12) (b) (3, 3) (c) (12, 13) (d) (26, 24)
  36. 36.What is the midpoint of the line joining (2, 0) and (6, 4)? (a) (2, 4) (b) (2, 2) (c) (8, 4) (d) (4, 2)
  37. 37.What is the distance between the points (7, 16) and (15, 1)? (a) 18 (b) 17 (c) 289 (d) 23
  38. 38.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 31 (c) 25 (d) 625
  39. 39.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 7 (c) 25 (d) 6
  40. 40.What is the midpoint of the line joining (2, 2) and (14, 0)? (a) (1, 8) (b) (6, 1) (c) (16, 2) (d) (8, 1)

Answer key

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

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