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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 892 · 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 (3, 7) and (11, 1)? (a) 14 (b) 10 (c) 100 (d) 11
  2. 2.What is the distance between the points (1, 18) and (6, 6)? (a) 169 (b) 14 (c) 17 (d) 13
  3. 3.What is the distance between the points (5, 10) and (9, 7)? (a) 25 (b) 5 (c) 6 (d) 7
  4. 4.What is the midpoint of the line joining (9, 19) and (17, 9)? (a) (13, 14) (b) (14, 13) (c) (26, 28) (d) (4, 5)
  5. 5.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 100 (c) 14 (d) 11
  6. 6.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 15 (c) 16 (d) 225
  7. 7.What is the midpoint of the line joining (1, 4) and (11, 14)? (a) (6, 9) (b) (9, 6) (c) (12, 18) (d) (5, 5)
  8. 8.What is the midpoint of the line joining (5, 6) and (17, 16)? (a) (12, 11) (b) (22, 22) (c) (11, 11) (d) (6, 5)
  9. 9.What is the distance between the points (7, 13) and (19, 4)? (a) 225 (b) 16 (c) 21 (d) 15
  10. 10.What is the distance between the points (9, 9) and (24, 17)? (a) 289 (b) 18 (c) 17 (d) 23
  11. 11.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 13 (c) 14 (d) 17
  12. 12.What is the midpoint of the line joining (6, 12) and (18, 8)? (a) (6, 2) (b) (24, 20) (c) (10, 12) (d) (12, 10)
  13. 13.What is the distance between the points (9, 9) and (15, 1)? (a) 11 (b) 100 (c) 14 (d) 10
  14. 14.What is the midpoint of the line joining (0, 4) and (8, 6)? (a) (4, 1) (b) (5, 4) (c) (4, 5) (d) (8, 10)
  15. 15.What is the midpoint of the line joining (10, 4) and (18, 0)? (a) (4, 2) (b) (2, 14) (c) (28, 4) (d) (14, 2)
  16. 16.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 169 (c) 13 (d) 14
  17. 17.In which quadrant does the point (9, −5) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  18. 18.What is the distance between the points (2, 8) and (14, 24)? (a) 400 (b) 28 (c) 20 (d) 21
  19. 19.In which quadrant does the point (9, 1) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  20. 20.What is the distance between the points (1, 7) and (5, 10)? (a) 5 (b) 25 (c) 6 (d) 7
  21. 21.In which quadrant does the point (6, −2) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  22. 22.What is the midpoint of the line joining (5, 21) and (13, 9)? (a) (15, 9) (b) (18, 30) (c) (9, 15) (d) (4, 6)
  23. 23.What is the midpoint of the line joining (5, 7) and (9, 5)? (a) (6, 7) (b) (2, 1) (c) (14, 12) (d) (7, 6)
  24. 24.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 10 (c) 14 (d) 11
  25. 25.What is the midpoint of the line joining (8, 4) and (16, 14)? (a) (9, 12) (b) (4, 5) (c) (24, 18) (d) (12, 9)
  26. 26.In which quadrant does the point (−3, 5) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  27. 27.What is the distance between the points (4, 6) and (19, 14)? (a) 289 (b) 17 (c) 23 (d) 18
  28. 28.What is the midpoint of the line joining (0, 18) and (2, 10)? (a) (2, 28) (b) (14, 1) (c) (1, 14) (d) (1, 4)
  29. 29.What is the distance between the points (1, 12) and (10, 0)? (a) 15 (b) 16 (c) 21 (d) 225
  30. 30.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 25 (c) 7 (d) 5
  31. 31.What is the midpoint of the line joining (2, 15) and (6, 5)? (a) (10, 4) (b) (8, 20) (c) (4, 10) (d) (2, 5)
  32. 32.In which quadrant does the point (−1, 8) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  33. 33.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 25 (c) 26 (d) 625
  34. 34.What is the midpoint of the line joining (4, 8) and (6, 12)? (a) (10, 20) (b) (10, 5) (c) (1, 2) (d) (5, 10)
  35. 35.In which quadrant does the point (5, 2) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  36. 36.In which quadrant does the point (−1, 7) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  37. 37.In which quadrant does the point (1, −6) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  38. 38.What is the distance between the points (6, 1) and (12, 9)? (a) 14 (b) 100 (c) 10 (d) 11
  39. 39.What is the midpoint of the line joining (1, 10) and (5, 4)? (a) (3, 7) (b) (7, 3) (c) (2, 3) (d) (6, 14)
  40. 40.What is the distance between the points (8, 21) and (24, 9)? (a) 400 (b) 28 (c) 20 (d) 21

Answer key

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

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