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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 173 · 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.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 11 (c) 14 (d) 10
  2. 2.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 15 (c) 225 (d) 16
  3. 3.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 6 (c) 25 (d) 7
  4. 4.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 169 (c) 14 (d) 13
  5. 5.In which quadrant does the point (−9, 6) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  6. 6.In which quadrant does the point (−3, 5) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  7. 7.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 400 (c) 20 (d) 28
  8. 8.What is the distance between the points (0, 6) and (8, 21)? (a) 289 (b) 18 (c) 17 (d) 23
  9. 9.What is the distance between the points (3, 14) and (11, 8)? (a) 11 (b) 10 (c) 14 (d) 100
  10. 10.What is the midpoint of the line joining (0, 14) and (12, 4)? (a) (9, 6) (b) (6, 5) (c) (12, 18) (d) (6, 9)
  11. 11.What is the distance between the points (1, 13) and (25, 6)? (a) 625 (b) 31 (c) 25 (d) 26
  12. 12.What is the midpoint of the line joining (2, 2) and (10, 14)? (a) (6, 8) (b) (8, 6) (c) (4, 6) (d) (12, 16)
  13. 13.What is the distance between the points (1, 5) and (9, 11)? (a) 100 (b) 11 (c) 10 (d) 14
  14. 14.What is the distance between the points (6, 0) and (30, 7)? (a) 625 (b) 25 (c) 26 (d) 31
  15. 15.In which quadrant does the point (5, −5) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  16. 16.What is the midpoint of the line joining (7, 4) and (15, 12)? (a) (11, 8) (b) (22, 16) (c) (8, 11) (d) (4, 4)
  17. 17.What is the midpoint of the line joining (6, 5) and (14, 3)? (a) (4, 1) (b) (20, 8) (c) (10, 4) (d) (4, 10)
  18. 18.What is the midpoint of the line joining (6, 8) and (16, 2)? (a) (5, 11) (b) (5, 3) (c) (11, 5) (d) (22, 10)
  19. 19.What is the midpoint of the line joining (4, 9) and (14, 11)? (a) (5, 1) (b) (10, 9) (c) (9, 10) (d) (18, 20)
  20. 20.In which quadrant does the point (1, 4) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  21. 21.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 289 (c) 17 (d) 18
  22. 22.What is the distance between the points (2, 6) and (14, 11)? (a) 17 (b) 169 (c) 14 (d) 13
  23. 23.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 26 (c) 25 (d) 625
  24. 24.What is the midpoint of the line joining (1, 0) and (5, 6)? (a) (3, 3) (b) (6, 6) (c) (2, 3) (d) (4, 3)
  25. 25.What is the distance between the points (9, 9) and (25, 21)? (a) 400 (b) 20 (c) 21 (d) 28
  26. 26.How far is the point (12, 9) from the origin (0, 0)? (a) 16 (b) 21 (c) 225 (d) 15
  27. 27.What is the distance between the points (4, 13) and (13, 1)? (a) 15 (b) 21 (c) 16 (d) 225
  28. 28.What is the distance between the points (2, 12) and (14, 3)? (a) 21 (b) 15 (c) 225 (d) 16
  29. 29.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 289 (c) 23 (d) 17
  30. 30.What is the distance between the points (1, 9) and (13, 0)? (a) 15 (b) 225 (c) 16 (d) 21
  31. 31.What is the midpoint of the line joining (4, 16) and (14, 4)? (a) (5, 6) (b) (10, 9) (c) (9, 10) (d) (18, 20)
  32. 32.In which quadrant does the point (−9, 8) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  33. 33.What is the midpoint of the line joining (5, 2) and (13, 8)? (a) (18, 10) (b) (5, 9) (c) (9, 5) (d) (4, 3)
  34. 34.What is the distance between the points (8, 6) and (24, 18)? (a) 21 (b) 20 (c) 28 (d) 400
  35. 35.What is the distance between the points (1, 7) and (6, 19)? (a) 169 (b) 17 (c) 13 (d) 14
  36. 36.In which quadrant does the point (−2, 4) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  37. 37.In which quadrant does the point (−8, −9) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  38. 38.In which quadrant does the point (8, −6) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  39. 39.What is the distance between the points (7, 4) and (16, 16)? (a) 21 (b) 225 (c) 15 (d) 16
  40. 40.In which quadrant does the point (4, −1) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant

Answer key

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

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