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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 599 · 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) 14 (c) 10 (d) 11
  2. 2.What is the midpoint of the line joining (6, 6) and (8, 10)? (a) (14, 16) (b) (1, 2) (c) (7, 8) (d) (8, 7)
  3. 3.In which quadrant does the point (−9, 2) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  4. 4.What is the distance between the points (1, 2) and (4, 6)? (a) 6 (b) 7 (c) 25 (d) 5
  5. 5.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 14 (c) 10 (d) 100
  6. 6.What is the midpoint of the line joining (10, 11) and (20, 1)? (a) (15, 6) (b) (30, 12) (c) (5, 5) (d) (6, 15)
  7. 7.What is the midpoint of the line joining (6, 4) and (18, 8)? (a) (6, 12) (b) (24, 12) (c) (12, 6) (d) (6, 2)
  8. 8.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 18 (c) 17 (d) 289
  9. 9.What is the distance between the points (4, 9) and (12, 3)? (a) 10 (b) 11 (c) 14 (d) 100
  10. 10.In which quadrant does the point (−2, 2) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  11. 11.What is the midpoint of the line joining (1, 6) and (9, 10)? (a) (10, 16) (b) (4, 2) (c) (5, 8) (d) (8, 5)
  12. 12.What is the midpoint of the line joining (7, 7) and (15, 1)? (a) (4, 3) (b) (11, 4) (c) (22, 8) (d) (4, 11)
  13. 13.What is the distance between the points (1, 11) and (5, 8)? (a) 25 (b) 6 (c) 5 (d) 7
  14. 14.What is the midpoint of the line joining (1, 11) and (9, 9)? (a) (5, 10) (b) (10, 20) (c) (4, 1) (d) (10, 5)
  15. 15.What is the distance between the points (0, 24) and (12, 8)? (a) 20 (b) 21 (c) 28 (d) 400
  16. 16.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 400 (c) 21 (d) 20
  17. 17.What is the distance between the points (5, 3) and (8, 7)? (a) 25 (b) 7 (c) 6 (d) 5
  18. 18.What is the distance between the points (4, 30) and (11, 6)? (a) 31 (b) 26 (c) 625 (d) 25
  19. 19.What is the distance between the points (6, 16) and (11, 4)? (a) 13 (b) 169 (c) 17 (d) 14
  20. 20.What is the distance between the points (5, 2) and (8, 6)? (a) 7 (b) 6 (c) 25 (d) 5
  21. 21.What is the midpoint of the line joining (7, 8) and (19, 20)? (a) (26, 28) (b) (14, 13) (c) (13, 14) (d) (6, 6)
  22. 22.In which quadrant does the point (−7, −9) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  23. 23.In which quadrant does the point (2, −9) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  24. 24.In which quadrant does the point (−9, −6) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  25. 25.What is the distance between the points (2, 16) and (18, 4)? (a) 28 (b) 21 (c) 20 (d) 400
  26. 26.What is the distance between the points (3, 10) and (11, 4)? (a) 100 (b) 11 (c) 14 (d) 10
  27. 27.What is the distance between the points (9, 17) and (15, 9)? (a) 14 (b) 100 (c) 11 (d) 10
  28. 28.What is the distance between the points (3, 13) and (15, 4)? (a) 225 (b) 15 (c) 16 (d) 21
  29. 29.How far is the point (12, 9) from the origin (0, 0)? (a) 15 (b) 225 (c) 16 (d) 21
  30. 30.What is the distance between the points (1, 23) and (13, 7)? (a) 28 (b) 21 (c) 400 (d) 20
  31. 31.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 169 (c) 14 (d) 13
  32. 32.In which quadrant does the point (6, 5) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  33. 33.In which quadrant does the point (4, 2) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  34. 34.What is the distance between the points (7, 16) and (19, 7)? (a) 15 (b) 21 (c) 16 (d) 225
  35. 35.What is the distance between the points (1, 16) and (9, 1)? (a) 289 (b) 18 (c) 17 (d) 23
  36. 36.What is the midpoint of the line joining (2, 1) and (14, 13)? (a) (8, 7) (b) (16, 14) (c) (7, 8) (d) (6, 6)
  37. 37.What is the midpoint of the line joining (0, 15) and (12, 5)? (a) (10, 6) (b) (12, 20) (c) (6, 10) (d) (6, 5)
  38. 38.In which quadrant does the point (9, 1) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  39. 39.What is the midpoint of the line joining (2, 6) and (8, 2)? (a) (5, 4) (b) (3, 2) (c) (4, 5) (d) (10, 8)
  40. 40.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 225 (c) 15 (d) 16

Answer key

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

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