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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 669 · 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, −2) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  2. 2.What is the distance between the points (1, 2) and (5, 5)? (a) 6 (b) 7 (c) 25 (d) 5
  3. 3.What is the midpoint of the line joining (0, 0) and (2, 2)? (a) (1, 2) (b) (2, 2) (c) (1, 1) (d) (2, 1)
  4. 4.What is the midpoint of the line joining (5, 17) and (13, 9)? (a) (4, 4) (b) (18, 26) (c) (9, 13) (d) (13, 9)
  5. 5.What is the midpoint of the line joining (1, 19) and (5, 9)? (a) (3, 14) (b) (2, 5) (c) (6, 28) (d) (14, 3)
  6. 6.In which quadrant does the point (−1, −1) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  7. 7.In which quadrant does the point (−4, −9) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  8. 8.What is the distance between the points (9, 0) and (24, 8)? (a) 17 (b) 289 (c) 23 (d) 18
  9. 9.In which quadrant does the point (−6, 5) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  10. 10.In which quadrant does the point (1, 3) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  11. 11.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 25 (c) 5 (d) 7
  12. 12.What is the midpoint of the line joining (0, 2) and (12, 14)? (a) (6, 6) (b) (8, 6) (c) (12, 16) (d) (6, 8)
  13. 13.In which quadrant does the point (−7, 8) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  14. 14.What is the distance between the points (9, 6) and (24, 14)? (a) 289 (b) 23 (c) 17 (d) 18
  15. 15.What is the midpoint of the line joining (4, 14) and (12, 8)? (a) (16, 22) (b) (11, 8) (c) (4, 3) (d) (8, 11)
  16. 16.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 31 (c) 25 (d) 26
  17. 17.What is the midpoint of the line joining (0, 0) and (2, 10)? (a) (5, 1) (b) (1, 5) (c) (2, 5) (d) (2, 10)
  18. 18.How far is the point (12, 9) from the origin (0, 0)? (a) 15 (b) 16 (c) 225 (d) 21
  19. 19.What is the midpoint of the line joining (2, 6) and (8, 16)? (a) (3, 5) (b) (11, 5) (c) (5, 11) (d) (10, 22)
  20. 20.What is the distance between the points (1, 8) and (13, 3)? (a) 17 (b) 169 (c) 13 (d) 14
  21. 21.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 169 (c) 14 (d) 13
  22. 22.In which quadrant does the point (−1, 1) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  23. 23.In which quadrant does the point (−4, 9) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  24. 24.What is the distance between the points (8, 18) and (16, 3)? (a) 18 (b) 17 (c) 289 (d) 23
  25. 25.What is the distance between the points (5, 1) and (13, 7)? (a) 14 (b) 10 (c) 11 (d) 100
  26. 26.In which quadrant does the point (−9, 5) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  27. 27.What is the distance between the points (2, 12) and (11, 0)? (a) 16 (b) 225 (c) 15 (d) 21
  28. 28.What is the distance between the points (9, 7) and (12, 3)? (a) 6 (b) 5 (c) 7 (d) 25
  29. 29.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 11 (c) 10 (d) 14
  30. 30.In which quadrant does the point (−9, 1) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  31. 31.What is the midpoint of the line joining (5, 13) and (11, 1)? (a) (16, 14) (b) (7, 8) (c) (3, 6) (d) (8, 7)
  32. 32.What is the midpoint of the line joining (2, 5) and (4, 15)? (a) (3, 10) (b) (6, 20) (c) (10, 3) (d) (1, 5)
  33. 33.What is the midpoint of the line joining (10, 10) and (14, 4)? (a) (2, 3) (b) (12, 7) (c) (24, 14) (d) (7, 12)
  34. 34.In which quadrant does the point (9, 6) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  35. 35.What is the distance between the points (9, 15) and (21, 6)? (a) 225 (b) 16 (c) 15 (d) 21
  36. 36.In which quadrant does the point (−3, −3) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  37. 37.What is the midpoint of the line joining (8, 10) and (16, 2)? (a) (12, 6) (b) (4, 4) (c) (6, 12) (d) (24, 12)
  38. 38.In which quadrant does the point (−2, 5) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  39. 39.What is the midpoint of the line joining (7, 4) and (11, 12)? (a) (2, 4) (b) (18, 16) (c) (9, 8) (d) (8, 9)
  40. 40.What is the distance between the points (4, 7) and (7, 3)? (a) 6 (b) 7 (c) 25 (d) 5

Answer key

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

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