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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 308 · 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 (9, −8) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  2. 2.What is the distance between the points (2, 16) and (26, 9)? (a) 31 (b) 26 (c) 625 (d) 25
  3. 3.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 26 (c) 31 (d) 25
  4. 4.In which quadrant does the point (6, 5) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  5. 5.What is the distance between the points (7, 10) and (10, 6)? (a) 6 (b) 5 (c) 7 (d) 25
  6. 6.What is the midpoint of the line joining (3, 15) and (13, 3)? (a) (5, 6) (b) (16, 18) (c) (9, 8) (d) (8, 9)
  7. 7.In which quadrant does the point (−5, −7) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  8. 8.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 21 (c) 225 (d) 15
  9. 9.In which quadrant does the point (7, −8) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  10. 10.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 7 (c) 25 (d) 5
  11. 11.What is the midpoint of the line joining (10, 9) and (12, 11)? (a) (1, 1) (b) (22, 20) (c) (11, 10) (d) (10, 11)
  12. 12.What is the distance between the points (7, 1) and (19, 17)? (a) 400 (b) 21 (c) 28 (d) 20
  13. 13.What is the midpoint of the line joining (4, 9) and (8, 7)? (a) (6, 8) (b) (2, 1) (c) (8, 6) (d) (12, 16)
  14. 14.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 31 (c) 26 (d) 25
  15. 15.In which quadrant does the point (−1, −9) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  16. 16.In which quadrant does the point (−4, 5) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  17. 17.What is the midpoint of the line joining (8, 6) and (16, 8)? (a) (4, 1) (b) (24, 14) (c) (7, 12) (d) (12, 7)
  18. 18.What is the distance between the points (0, 8) and (6, 0)? (a) 14 (b) 100 (c) 10 (d) 11
  19. 19.What is the distance between the points (7, 2) and (16, 14)? (a) 16 (b) 21 (c) 225 (d) 15
  20. 20.What is the midpoint of the line joining (5, 3) and (15, 13)? (a) (10, 8) (b) (8, 10) (c) (20, 16) (d) (5, 5)
  21. 21.What is the distance between the points (4, 4) and (9, 16)? (a) 169 (b) 17 (c) 13 (d) 14
  22. 22.What is the midpoint of the line joining (0, 7) and (4, 11)? (a) (4, 18) (b) (2, 9) (c) (2, 2) (d) (9, 2)
  23. 23.What is the midpoint of the line joining (2, 7) and (12, 3)? (a) (5, 7) (b) (5, 2) (c) (14, 10) (d) (7, 5)
  24. 24.What is the midpoint of the line joining (8, 15) and (10, 3)? (a) (18, 18) (b) (1, 6) (c) (10, 9) (d) (9, 9)
  25. 25.What is the distance between the points (8, 2) and (20, 7)? (a) 17 (b) 14 (c) 13 (d) 169
  26. 26.In which quadrant does the point (−4, 9) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  27. 27.What is the distance between the points (3, 13) and (12, 1)? (a) 15 (b) 21 (c) 16 (d) 225
  28. 28.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 20 (c) 21 (d) 400
  29. 29.In which quadrant does the point (9, 7) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  30. 30.How far is the point (5, 12) from the origin (0, 0)? (a) 13 (b) 17 (c) 169 (d) 14
  31. 31.What is the midpoint of the line joining (7, 8) and (13, 14)? (a) (10, 11) (b) (11, 10) (c) (3, 3) (d) (20, 22)
  32. 32.In which quadrant does the point (−1, −6) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  33. 33.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 7 (c) 6 (d) 25
  34. 34.What is the midpoint of the line joining (7, 12) and (9, 6)? (a) (9, 8) (b) (1, 3) (c) (16, 18) (d) (8, 9)
  35. 35.In which quadrant does the point (−7, −8) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  36. 36.What is the distance between the points (9, 7) and (21, 23)? (a) 20 (b) 28 (c) 400 (d) 21
  37. 37.What is the midpoint of the line joining (3, 1) and (11, 5)? (a) (14, 6) (b) (4, 2) (c) (7, 3) (d) (3, 7)
  38. 38.In which quadrant does the point (2, −9) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  39. 39.What is the midpoint of the line joining (7, 9) and (9, 15)? (a) (16, 24) (b) (8, 12) (c) (1, 3) (d) (12, 8)
  40. 40.In which quadrant does the point (6, −7) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant

Answer key

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

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