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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 283 · 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, −4) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  2. 2.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 6 (c) 25 (d) 5
  3. 3.How far is the point (15, 8) from the origin (0, 0)? (a) 17 (b) 289 (c) 18 (d) 23
  4. 4.What is the midpoint of the line joining (4, 6) and (12, 18)? (a) (16, 24) (b) (12, 8) (c) (4, 6) (d) (8, 12)
  5. 5.In which quadrant does the point (−6, 5) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  6. 6.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 400 (c) 21 (d) 20
  7. 7.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 20 (c) 21 (d) 28
  8. 8.How far is the point (5, 12) from the origin (0, 0)? (a) 13 (b) 14 (c) 17 (d) 169
  9. 9.In which quadrant does the point (7, 5) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  10. 10.What is the distance between the points (8, 11) and (11, 7)? (a) 7 (b) 6 (c) 5 (d) 25
  11. 11.In which quadrant does the point (4, 4) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  12. 12.What is the midpoint of the line joining (3, 4) and (11, 0)? (a) (7, 2) (b) (14, 4) (c) (4, 2) (d) (2, 7)
  13. 13.How far is the point (4, 3) from the origin (0, 0)? (a) 5 (b) 25 (c) 6 (d) 7
  14. 14.What is the midpoint of the line joining (10, 6) and (20, 4)? (a) (5, 15) (b) (30, 10) (c) (15, 5) (d) (5, 1)
  15. 15.In which quadrant does the point (5, 3) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  16. 16.What is the distance between the points (6, 9) and (15, 21)? (a) 15 (b) 16 (c) 225 (d) 21
  17. 17.What is the distance between the points (3, 3) and (11, 9)? (a) 14 (b) 10 (c) 11 (d) 100
  18. 18.What is the distance between the points (2, 3) and (6, 6)? (a) 5 (b) 6 (c) 25 (d) 7
  19. 19.What is the midpoint of the line joining (4, 3) and (14, 1)? (a) (18, 4) (b) (2, 9) (c) (9, 2) (d) (5, 1)
  20. 20.What is the distance between the points (5, 3) and (8, 7)? (a) 25 (b) 7 (c) 5 (d) 6
  21. 21.How far is the point (12, 5) from the origin (0, 0)? (a) 13 (b) 17 (c) 14 (d) 169
  22. 22.In which quadrant does the point (6, −2) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  23. 23.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 14 (c) 100 (d) 11
  24. 24.In which quadrant does the point (−6, −6) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  25. 25.What is the midpoint of the line joining (2, 10) and (8, 6)? (a) (5, 8) (b) (8, 5) (c) (3, 2) (d) (10, 16)
  26. 26.In which quadrant does the point (−1, 4) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  27. 27.What is the distance between the points (3, 8) and (15, 17)? (a) 21 (b) 15 (c) 16 (d) 225
  28. 28.What is the distance between the points (7, 14) and (13, 6)? (a) 100 (b) 11 (c) 14 (d) 10
  29. 29.What is the distance between the points (6, 11) and (18, 6)? (a) 14 (b) 169 (c) 13 (d) 17
  30. 30.What is the distance between the points (6, 4) and (14, 19)? (a) 289 (b) 17 (c) 23 (d) 18
  31. 31.What is the midpoint of the line joining (9, 5) and (21, 11)? (a) (6, 3) (b) (30, 16) (c) (15, 8) (d) (8, 15)
  32. 32.What is the distance between the points (9, 14) and (15, 6)? (a) 14 (b) 11 (c) 10 (d) 100
  33. 33.What is the midpoint of the line joining (8, 5) and (10, 15)? (a) (10, 9) (b) (9, 10) (c) (1, 5) (d) (18, 20)
  34. 34.In which quadrant does the point (2, 2) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  35. 35.What is the midpoint of the line joining (4, 11) and (8, 1)? (a) (7, 6) (b) (12, 12) (c) (6, 6) (d) (2, 5)
  36. 36.What is the distance between the points (4, 4) and (8, 1)? (a) 6 (b) 5 (c) 25 (d) 7
  37. 37.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 14 (c) 11 (d) 100
  38. 38.What is the distance between the points (0, 4) and (6, 12)? (a) 11 (b) 14 (c) 10 (d) 100
  39. 39.In which quadrant does the point (−2, 2) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  40. 40.In which quadrant does the point (−7, −3) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant

Answer key

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

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