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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 597 · 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.In which quadrant does the point (−9, 5) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  2. 2.What is the midpoint of the line joining (8, 17) and (14, 7)? (a) (3, 5) (b) (12, 11) (c) (22, 24) (d) (11, 12)
  3. 3.What is the distance between the points (2, 4) and (8, 12)? (a) 10 (b) 100 (c) 14 (d) 11
  4. 4.In which quadrant does the point (4, 1) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  5. 5.What is the distance between the points (6, 8) and (9, 4)? (a) 7 (b) 6 (c) 5 (d) 25
  6. 6.In which quadrant does the point (5, −4) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  7. 7.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 625 (c) 26 (d) 25
  8. 8.What is the midpoint of the line joining (10, 7) and (14, 1)? (a) (24, 8) (b) (2, 3) (c) (12, 4) (d) (4, 12)
  9. 9.What is the distance between the points (7, 7) and (10, 11)? (a) 25 (b) 7 (c) 5 (d) 6
  10. 10.What is the distance between the points (8, 3) and (16, 9)? (a) 10 (b) 100 (c) 14 (d) 11
  11. 11.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 18 (c) 289 (d) 17
  12. 12.What is the midpoint of the line joining (3, 0) and (7, 10)? (a) (5, 5) (b) (10, 10) (c) (6, 5) (d) (2, 5)
  13. 13.What is the midpoint of the line joining (10, 11) and (22, 3)? (a) (6, 4) (b) (16, 7) (c) (32, 14) (d) (7, 16)
  14. 14.In which quadrant does the point (2, 5) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  15. 15.What is the distance between the points (0, 20) and (8, 5)? (a) 23 (b) 17 (c) 289 (d) 18
  16. 16.What is the midpoint of the line joining (9, 10) and (11, 20)? (a) (20, 30) (b) (15, 10) (c) (1, 5) (d) (10, 15)
  17. 17.How far is the point (12, 9) from the origin (0, 0)? (a) 16 (b) 225 (c) 21 (d) 15
  18. 18.What is the midpoint of the line joining (3, 11) and (11, 3)? (a) (14, 14) (b) (4, 4) (c) (8, 7) (d) (7, 7)
  19. 19.In which quadrant does the point (5, −8) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  20. 20.In which quadrant does the point (4, 9) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  21. 21.What is the midpoint of the line joining (5, 4) and (9, 2)? (a) (7, 3) (b) (3, 7) (c) (2, 1) (d) (14, 6)
  22. 22.In which quadrant does the point (−1, 7) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  23. 23.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 28 (c) 21 (d) 400
  24. 24.What is the distance between the points (0, 9) and (4, 12)? (a) 7 (b) 5 (c) 25 (d) 6
  25. 25.What is the midpoint of the line joining (10, 5) and (18, 11)? (a) (14, 8) (b) (4, 3) (c) (28, 16) (d) (8, 14)
  26. 26.What is the midpoint of the line joining (10, 9) and (16, 13)? (a) (11, 13) (b) (3, 2) (c) (26, 22) (d) (13, 11)
  27. 27.In which quadrant does the point (−3, −1) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  28. 28.What is the midpoint of the line joining (6, 8) and (16, 12)? (a) (5, 2) (b) (22, 20) (c) (10, 11) (d) (11, 10)
  29. 29.What is the midpoint of the line joining (7, 3) and (9, 5)? (a) (4, 8) (b) (16, 8) (c) (8, 4) (d) (1, 1)
  30. 30.How far is the point (24, 7) from the origin (0, 0)? (a) 25 (b) 26 (c) 625 (d) 31
  31. 31.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 5 (c) 6 (d) 25
  32. 32.What is the midpoint of the line joining (10, 12) and (20, 4)? (a) (8, 15) (b) (30, 16) (c) (5, 4) (d) (15, 8)
  33. 33.In which quadrant does the point (2, 8) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  34. 34.What is the midpoint of the line joining (0, 2) and (2, 14)? (a) (2, 16) (b) (1, 6) (c) (1, 8) (d) (8, 1)
  35. 35.What is the midpoint of the line joining (9, 15) and (13, 3)? (a) (9, 11) (b) (2, 6) (c) (11, 9) (d) (22, 18)
  36. 36.What is the midpoint of the line joining (10, 0) and (22, 4)? (a) (32, 4) (b) (16, 2) (c) (6, 2) (d) (2, 16)
  37. 37.What is the distance between the points (0, 2) and (8, 8)? (a) 100 (b) 14 (c) 11 (d) 10
  38. 38.What is the distance between the points (7, 26) and (14, 2)? (a) 26 (b) 625 (c) 25 (d) 31
  39. 39.In which quadrant does the point (−3, 5) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  40. 40.What is the distance between the points (5, 2) and (14, 14)? (a) 225 (b) 15 (c) 21 (d) 16

Answer key

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

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