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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 722 · 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 (6, 7) and (14, 17)? (a) (12, 10) (b) (10, 12) (c) (4, 5) (d) (20, 24)
  2. 2.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 17 (c) 23 (d) 289
  3. 3.What is the midpoint of the line joining (0, 9) and (2, 13)? (a) (11, 1) (b) (1, 11) (c) (2, 22) (d) (1, 2)
  4. 4.In which quadrant does the point (−5, −9) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  5. 5.What is the distance between the points (5, 5) and (13, 20)? (a) 289 (b) 18 (c) 17 (d) 23
  6. 6.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 17 (c) 18 (d) 23
  7. 7.What is the midpoint of the line joining (4, 10) and (10, 22)? (a) (14, 32) (b) (7, 16) (c) (3, 6) (d) (16, 7)
  8. 8.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 100 (c) 14 (d) 10
  9. 9.What is the distance between the points (4, 11) and (12, 5)? (a) 11 (b) 10 (c) 14 (d) 100
  10. 10.What is the midpoint of the line joining (1, 0) and (5, 12)? (a) (3, 6) (b) (6, 12) (c) (6, 3) (d) (2, 6)
  11. 11.What is the distance between the points (2, 4) and (10, 19)? (a) 23 (b) 18 (c) 17 (d) 289
  12. 12.What is the midpoint of the line joining (1, 9) and (5, 7)? (a) (2, 1) (b) (3, 8) (c) (6, 16) (d) (8, 3)
  13. 13.What is the distance between the points (6, 7) and (14, 13)? (a) 14 (b) 11 (c) 10 (d) 100
  14. 14.What is the distance between the points (2, 1) and (26, 8)? (a) 25 (b) 625 (c) 26 (d) 31
  15. 15.What is the distance between the points (2, 0) and (9, 24)? (a) 625 (b) 25 (c) 31 (d) 26
  16. 16.What is the distance between the points (9, 2) and (15, 10)? (a) 11 (b) 100 (c) 14 (d) 10
  17. 17.What is the distance between the points (8, 15) and (14, 7)? (a) 10 (b) 14 (c) 11 (d) 100
  18. 18.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 14 (c) 100 (d) 11
  19. 19.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 20 (c) 21 (d) 400
  20. 20.What is the distance between the points (1, 12) and (7, 4)? (a) 14 (b) 11 (c) 100 (d) 10
  21. 21.What is the distance between the points (6, 5) and (15, 17)? (a) 21 (b) 15 (c) 16 (d) 225
  22. 22.In which quadrant does the point (−2, 6) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  23. 23.In which quadrant does the point (7, 2) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  24. 24.What is the midpoint of the line joining (1, 7) and (3, 17)? (a) (12, 2) (b) (1, 5) (c) (2, 12) (d) (4, 24)
  25. 25.What is the distance between the points (5, 8) and (17, 24)? (a) 400 (b) 20 (c) 21 (d) 28
  26. 26.What is the distance between the points (2, 16) and (7, 4)? (a) 169 (b) 13 (c) 14 (d) 17
  27. 27.In which quadrant does the point (8, −2) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  28. 28.What is the distance between the points (7, 4) and (22, 12)? (a) 289 (b) 17 (c) 18 (d) 23
  29. 29.What is the midpoint of the line joining (1, 8) and (3, 14)? (a) (11, 2) (b) (4, 22) (c) (1, 3) (d) (2, 11)
  30. 30.What is the midpoint of the line joining (9, 3) and (15, 5)? (a) (24, 8) (b) (4, 12) (c) (3, 1) (d) (12, 4)
  31. 31.What is the midpoint of the line joining (2, 3) and (8, 15)? (a) (10, 18) (b) (9, 5) (c) (3, 6) (d) (5, 9)
  32. 32.What is the midpoint of the line joining (8, 3) and (20, 5)? (a) (28, 8) (b) (14, 4) (c) (4, 14) (d) (6, 1)
  33. 33.What is the distance between the points (1, 1) and (6, 13)? (a) 17 (b) 169 (c) 13 (d) 14
  34. 34.What is the distance between the points (3, 18) and (12, 6)? (a) 225 (b) 15 (c) 16 (d) 21
  35. 35.What is the midpoint of the line joining (2, 6) and (10, 18)? (a) (12, 6) (b) (4, 6) (c) (12, 24) (d) (6, 12)
  36. 36.What is the midpoint of the line joining (4, 18) and (10, 8)? (a) (13, 7) (b) (3, 5) (c) (14, 26) (d) (7, 13)
  37. 37.What is the distance between the points (0, 13) and (5, 1)? (a) 169 (b) 14 (c) 17 (d) 13
  38. 38.In which quadrant does the point (5, 5) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  39. 39.What is the midpoint of the line joining (6, 4) and (12, 10)? (a) (3, 3) (b) (7, 9) (c) (9, 7) (d) (18, 14)
  40. 40.What is the midpoint of the line joining (4, 6) and (6, 14)? (a) (10, 20) (b) (1, 4) (c) (10, 5) (d) (5, 10)

Answer key

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

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