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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 326 · 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.What is the midpoint of the line joining (1, 6) and (9, 12)? (a) (5, 9) (b) (10, 18) (c) (4, 3) (d) (9, 5)
  2. 2.What is the midpoint of the line joining (9, 12) and (21, 8)? (a) (10, 15) (b) (6, 2) (c) (30, 20) (d) (15, 10)
  3. 3.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 289 (c) 17 (d) 23
  4. 4.In which quadrant does the point (−7, 3) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  5. 5.What is the distance between the points (3, 7) and (12, 19)? (a) 21 (b) 16 (c) 225 (d) 15
  6. 6.What is the midpoint of the line joining (7, 3) and (9, 11)? (a) (7, 8) (b) (16, 14) (c) (1, 4) (d) (8, 7)
  7. 7.What is the distance between the points (3, 4) and (6, 0)? (a) 7 (b) 25 (c) 6 (d) 5
  8. 8.What is the midpoint of the line joining (1, 2) and (13, 8)? (a) (14, 10) (b) (5, 7) (c) (7, 5) (d) (6, 3)
  9. 9.In which quadrant does the point (−2, 5) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  10. 10.What is the distance between the points (6, 9) and (9, 13)? (a) 6 (b) 25 (c) 7 (d) 5
  11. 11.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 169 (c) 13 (d) 17
  12. 12.In which quadrant does the point (6, 8) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  13. 13.In which quadrant does the point (2, 2) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  14. 14.What is the distance between the points (7, 8) and (19, 24)? (a) 400 (b) 20 (c) 28 (d) 21
  15. 15.What is the midpoint of the line joining (0, 8) and (6, 18)? (a) (6, 26) (b) (3, 13) (c) (13, 3) (d) (3, 5)
  16. 16.What is the distance between the points (6, 2) and (18, 18)? (a) 20 (b) 21 (c) 400 (d) 28
  17. 17.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 11 (c) 100 (d) 10
  18. 18.What is the distance between the points (2, 9) and (17, 17)? (a) 289 (b) 23 (c) 18 (d) 17
  19. 19.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 18 (c) 17 (d) 23
  20. 20.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 7 (c) 5 (d) 6
  21. 21.In which quadrant does the point (8, 9) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  22. 22.In which quadrant does the point (5, 7) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  23. 23.In which quadrant does the point (6, −7) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  24. 24.In which quadrant does the point (3, −5) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  25. 25.What is the distance between the points (3, 31) and (10, 7)? (a) 26 (b) 25 (c) 31 (d) 625
  26. 26.What is the distance between the points (3, 7) and (11, 22)? (a) 17 (b) 18 (c) 289 (d) 23
  27. 27.How far is the point (9, 12) from the origin (0, 0)? (a) 15 (b) 21 (c) 16 (d) 225
  28. 28.What is the distance between the points (6, 7) and (12, 15)? (a) 100 (b) 11 (c) 14 (d) 10
  29. 29.What is the midpoint of the line joining (9, 8) and (19, 20)? (a) (5, 6) (b) (14, 14) (c) (15, 14) (d) (28, 28)
  30. 30.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 400 (c) 20 (d) 21
  31. 31.What is the midpoint of the line joining (3, 9) and (5, 15)? (a) (12, 4) (b) (8, 24) (c) (1, 3) (d) (4, 12)
  32. 32.In which quadrant does the point (−4, −6) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  33. 33.What is the distance between the points (1, 25) and (8, 1)? (a) 25 (b) 31 (c) 625 (d) 26
  34. 34.In which quadrant does the point (7, −6) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  35. 35.What is the distance between the points (7, 10) and (19, 1)? (a) 16 (b) 21 (c) 15 (d) 225
  36. 36.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 5 (c) 6 (d) 7
  37. 37.What is the midpoint of the line joining (1, 17) and (9, 5)? (a) (11, 5) (b) (10, 22) (c) (5, 11) (d) (4, 6)
  38. 38.What is the midpoint of the line joining (5, 11) and (15, 1)? (a) (6, 10) (b) (10, 6) (c) (5, 5) (d) (20, 12)
  39. 39.In which quadrant does the point (3, 2) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  40. 40.In which quadrant does the point (−3, 8) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant

Answer key

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

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