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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 622 · 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 (4, 4) and (14, 8)? (a) (5, 2) (b) (18, 12) (c) (6, 9) (d) (9, 6)
  2. 2.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 10 (c) 100 (d) 11
  3. 3.What is the distance between the points (3, 2) and (9, 10)? (a) 100 (b) 11 (c) 14 (d) 10
  4. 4.What is the distance between the points (1, 13) and (10, 1)? (a) 16 (b) 21 (c) 225 (d) 15
  5. 5.What is the distance between the points (1, 12) and (25, 5)? (a) 26 (b) 31 (c) 625 (d) 25
  6. 6.What is the midpoint of the line joining (10, 8) and (18, 20)? (a) (14, 14) (b) (28, 28) (c) (15, 14) (d) (4, 6)
  7. 7.In which quadrant does the point (−1, 7) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  8. 8.What is the distance between the points (9, 8) and (13, 5)? (a) 6 (b) 7 (c) 5 (d) 25
  9. 9.What is the midpoint of the line joining (7, 13) and (9, 5)? (a) (16, 18) (b) (8, 9) (c) (9, 8) (d) (1, 4)
  10. 10.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 28 (c) 20 (d) 21
  11. 11.What is the midpoint of the line joining (8, 3) and (20, 7)? (a) (5, 14) (b) (14, 5) (c) (28, 10) (d) (6, 2)
  12. 12.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 21 (c) 225 (d) 15
  13. 13.What is the distance between the points (5, 10) and (8, 6)? (a) 25 (b) 6 (c) 5 (d) 7
  14. 14.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 25 (c) 26 (d) 625
  15. 15.What is the distance between the points (0, 4) and (12, 9)? (a) 169 (b) 13 (c) 17 (d) 14
  16. 16.What is the distance between the points (0, 9) and (12, 0)? (a) 21 (b) 15 (c) 225 (d) 16
  17. 17.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 225 (c) 15 (d) 16
  18. 18.How far is the point (5, 12) from the origin (0, 0)? (a) 13 (b) 14 (c) 17 (d) 169
  19. 19.What is the midpoint of the line joining (5, 12) and (7, 10)? (a) (12, 22) (b) (6, 11) (c) (1, 1) (d) (11, 6)
  20. 20.What is the distance between the points (0, 13) and (3, 9)? (a) 7 (b) 6 (c) 25 (d) 5
  21. 21.What is the distance between the points (3, 23) and (15, 7)? (a) 28 (b) 20 (c) 21 (d) 400
  22. 22.What is the distance between the points (5, 12) and (29, 5)? (a) 625 (b) 31 (c) 25 (d) 26
  23. 23.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 169 (c) 14 (d) 13
  24. 24.What is the midpoint of the line joining (8, 13) and (16, 9)? (a) (24, 22) (b) (4, 2) (c) (12, 11) (d) (11, 12)
  25. 25.What is the distance between the points (3, 22) and (11, 7)? (a) 17 (b) 23 (c) 289 (d) 18
  26. 26.In which quadrant does the point (6, 8) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  27. 27.What is the midpoint of the line joining (3, 6) and (9, 0)? (a) (12, 6) (b) (3, 3) (c) (3, 6) (d) (6, 3)
  28. 28.In which quadrant does the point (5, 1) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  29. 29.In which quadrant does the point (−6, 5) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  30. 30.What is the distance between the points (9, 33) and (16, 9)? (a) 26 (b) 25 (c) 625 (d) 31
  31. 31.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 10 (c) 100 (d) 14
  32. 32.What is the midpoint of the line joining (10, 10) and (22, 20)? (a) (6, 5) (b) (32, 30) (c) (16, 15) (d) (15, 16)
  33. 33.In which quadrant does the point (−6, 4) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  34. 34.In which quadrant does the point (−1, 9) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  35. 35.In which quadrant does the point (−3, −3) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  36. 36.In which quadrant does the point (−6, −9) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  37. 37.What is the distance between the points (8, 9) and (14, 1)? (a) 14 (b) 11 (c) 100 (d) 10
  38. 38.What is the midpoint of the line joining (6, 3) and (16, 1)? (a) (2, 11) (b) (22, 4) (c) (5, 1) (d) (11, 2)
  39. 39.What is the midpoint of the line joining (5, 5) and (13, 7)? (a) (6, 9) (b) (9, 6) (c) (4, 1) (d) (18, 12)
  40. 40.In which quadrant does the point (8, 7) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant

Answer key

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

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