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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 74 · 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 distance between the points (7, 3) and (15, 18)? (a) 17 (b) 18 (c) 289 (d) 23
  2. 2.What is the distance between the points (3, 7) and (27, 0)? (a) 31 (b) 625 (c) 26 (d) 25
  3. 3.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 23 (c) 17 (d) 18
  4. 4.In which quadrant does the point (−7, −8) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  5. 5.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 13 (c) 169 (d) 17
  6. 6.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 14 (c) 169 (d) 13
  7. 7.What is the distance between the points (9, 6) and (25, 18)? (a) 20 (b) 400 (c) 28 (d) 21
  8. 8.What is the midpoint of the line joining (1, 3) and (3, 15)? (a) (9, 2) (b) (2, 9) (c) (4, 18) (d) (1, 6)
  9. 9.In which quadrant does the point (8, 9) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  10. 10.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 5 (c) 7 (d) 25
  11. 11.In which quadrant does the point (−1, 6) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  12. 12.In which quadrant does the point (3, 3) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  13. 13.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 5 (c) 6 (d) 7
  14. 14.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 400 (c) 20 (d) 28
  15. 15.What is the distance between the points (9, 9) and (13, 12)? (a) 6 (b) 7 (c) 25 (d) 5
  16. 16.In which quadrant does the point (7, −5) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  17. 17.In which quadrant does the point (2, −3) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  18. 18.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 225 (c) 15 (d) 16
  19. 19.What is the distance between the points (1, 3) and (7, 11)? (a) 11 (b) 100 (c) 14 (d) 10
  20. 20.In which quadrant does the point (1, 4) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  21. 21.What is the midpoint of the line joining (9, 22) and (21, 10)? (a) (30, 32) (b) (15, 16) (c) (16, 15) (d) (6, 6)
  22. 22.What is the midpoint of the line joining (5, 5) and (9, 1)? (a) (7, 3) (b) (14, 6) (c) (3, 7) (d) (2, 2)
  23. 23.What is the distance between the points (1, 8) and (5, 5)? (a) 25 (b) 7 (c) 5 (d) 6
  24. 24.What is the midpoint of the line joining (2, 2) and (10, 10)? (a) (4, 4) (b) (12, 12) (c) (7, 6) (d) (6, 6)
  25. 25.What is the midpoint of the line joining (6, 2) and (12, 6)? (a) (3, 2) (b) (18, 8) (c) (4, 9) (d) (9, 4)
  26. 26.What is the midpoint of the line joining (1, 18) and (11, 8)? (a) (12, 26) (b) (13, 6) (c) (6, 13) (d) (5, 5)
  27. 27.What is the midpoint of the line joining (2, 0) and (10, 2)? (a) (12, 2) (b) (1, 6) (c) (6, 1) (d) (4, 1)
  28. 28.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 26 (c) 25 (d) 625
  29. 29.What is the distance between the points (0, 4) and (7, 28)? (a) 25 (b) 31 (c) 625 (d) 26
  30. 30.What is the midpoint of the line joining (8, 3) and (10, 15)? (a) (18, 18) (b) (9, 9) (c) (10, 9) (d) (1, 6)
  31. 31.What is the midpoint of the line joining (8, 8) and (12, 6)? (a) (7, 10) (b) (10, 7) (c) (2, 1) (d) (20, 14)
  32. 32.What is the distance between the points (8, 5) and (11, 1)? (a) 5 (b) 6 (c) 7 (d) 25
  33. 33.In which quadrant does the point (4, 1) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  34. 34.In which quadrant does the point (−9, −3) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  35. 35.In which quadrant does the point (4, 4) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  36. 36.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 100 (c) 14 (d) 11
  37. 37.What is the distance between the points (5, 7) and (8, 3)? (a) 6 (b) 5 (c) 25 (d) 7
  38. 38.How far is the point (24, 7) from the origin (0, 0)? (a) 26 (b) 25 (c) 625 (d) 31
  39. 39.What is the midpoint of the line joining (2, 1) and (10, 3)? (a) (4, 1) (b) (12, 4) (c) (6, 2) (d) (2, 6)
  40. 40.What is the distance between the points (7, 13) and (22, 5)? (a) 17 (b) 23 (c) 289 (d) 18

Answer key

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

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