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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 428 · 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 (2, 5) and (10, 17)? (a) (12, 22) (b) (6, 11) (c) (4, 6) (d) (11, 6)
  2. 2.What is the midpoint of the line joining (8, 8) and (14, 6)? (a) (3, 1) (b) (7, 11) (c) (11, 7) (d) (22, 14)
  3. 3.What is the midpoint of the line joining (7, 14) and (17, 2)? (a) (24, 16) (b) (12, 8) (c) (5, 6) (d) (8, 12)
  4. 4.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 21 (c) 20 (d) 28
  5. 5.What is the midpoint of the line joining (5, 8) and (11, 2)? (a) (5, 8) (b) (8, 5) (c) (16, 10) (d) (3, 3)
  6. 6.How far is the point (9, 12) from the origin (0, 0)? (a) 15 (b) 16 (c) 225 (d) 21
  7. 7.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 25 (c) 625 (d) 26
  8. 8.In which quadrant does the point (2, −5) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  9. 9.In which quadrant does the point (−2, 3) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  10. 10.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 100 (c) 11 (d) 10
  11. 11.In which quadrant does the point (6, −1) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  12. 12.What is the distance between the points (5, 13) and (13, 7)? (a) 10 (b) 100 (c) 14 (d) 11
  13. 13.How far is the point (15, 8) from the origin (0, 0)? (a) 17 (b) 18 (c) 289 (d) 23
  14. 14.How far is the point (24, 7) from the origin (0, 0)? (a) 26 (b) 25 (c) 31 (d) 625
  15. 15.In which quadrant does the point (7, 6) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  16. 16.What is the midpoint of the line joining (9, 12) and (19, 6)? (a) (9, 14) (b) (14, 9) (c) (28, 18) (d) (5, 3)
  17. 17.What is the midpoint of the line joining (7, 11) and (19, 7)? (a) (6, 2) (b) (26, 18) (c) (13, 9) (d) (9, 13)
  18. 18.What is the midpoint of the line joining (4, 14) and (16, 2)? (a) (20, 16) (b) (10, 8) (c) (6, 6) (d) (8, 10)
  19. 19.In which quadrant does the point (−6, 3) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  20. 20.What is the midpoint of the line joining (0, 9) and (2, 3)? (a) (6, 1) (b) (1, 3) (c) (1, 6) (d) (2, 12)
  21. 21.In which quadrant does the point (1, 3) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  22. 22.What is the midpoint of the line joining (6, 2) and (16, 10)? (a) (5, 4) (b) (11, 6) (c) (22, 12) (d) (6, 11)
  23. 23.In which quadrant does the point (−6, −8) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  24. 24.In which quadrant does the point (−8, −2) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  25. 25.What is the midpoint of the line joining (1, 16) and (7, 8)? (a) (3, 4) (b) (12, 4) (c) (4, 12) (d) (8, 24)
  26. 26.What is the midpoint of the line joining (0, 9) and (10, 1)? (a) (6, 5) (b) (5, 4) (c) (10, 10) (d) (5, 5)
  27. 27.What is the midpoint of the line joining (6, 1) and (10, 9)? (a) (2, 4) (b) (8, 5) (c) (16, 10) (d) (5, 8)
  28. 28.In which quadrant does the point (−1, 1) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  29. 29.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 25 (c) 6 (d) 7
  30. 30.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 100 (c) 14 (d) 10
  31. 31.How far is the point (16, 12) from the origin (0, 0)? (a) 400 (b) 21 (c) 20 (d) 28
  32. 32.What is the midpoint of the line joining (0, 0) and (6, 6)? (a) (4, 3) (b) (6, 6) (c) (3, 4) (d) (3, 3)
  33. 33.What is the distance between the points (1, 3) and (4, 7)? (a) 5 (b) 25 (c) 7 (d) 6
  34. 34.What is the distance between the points (9, 12) and (13, 9)? (a) 25 (b) 6 (c) 7 (d) 5
  35. 35.What is the distance between the points (2, 12) and (26, 5)? (a) 625 (b) 26 (c) 31 (d) 25
  36. 36.In which quadrant does the point (2, 9) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  37. 37.What is the distance between the points (1, 4) and (17, 16)? (a) 400 (b) 20 (c) 21 (d) 28
  38. 38.What is the distance between the points (9, 9) and (12, 5)? (a) 25 (b) 6 (c) 7 (d) 5
  39. 39.What is the midpoint of the line joining (5, 14) and (13, 4)? (a) (10, 9) (b) (18, 18) (c) (4, 5) (d) (9, 9)
  40. 40.In which quadrant does the point (−7, 3) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant

Answer key

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

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