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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 945 · 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 (−2, −1) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  2. 2.What is the distance between the points (8, 4) and (24, 16)? (a) 400 (b) 20 (c) 21 (d) 28
  3. 3.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 6 (c) 7 (d) 5
  4. 4.What is the midpoint of the line joining (6, 1) and (10, 13)? (a) (2, 6) (b) (7, 8) (c) (16, 14) (d) (8, 7)
  5. 5.How far is the point (24, 7) from the origin (0, 0)? (a) 25 (b) 625 (c) 26 (d) 31
  6. 6.In which quadrant does the point (−8, −9) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  7. 7.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 400 (c) 21 (d) 20
  8. 8.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 14 (c) 100 (d) 10
  9. 9.What is the distance between the points (3, 3) and (11, 18)? (a) 18 (b) 289 (c) 23 (d) 17
  10. 10.In which quadrant does the point (−5, −3) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  11. 11.What is the distance between the points (3, 12) and (11, 6)? (a) 100 (b) 11 (c) 10 (d) 14
  12. 12.What is the distance between the points (8, 6) and (20, 11)? (a) 169 (b) 14 (c) 13 (d) 17
  13. 13.What is the midpoint of the line joining (8, 10) and (16, 12)? (a) (11, 12) (b) (12, 11) (c) (4, 1) (d) (24, 22)
  14. 14.What is the distance between the points (1, 0) and (9, 6)? (a) 11 (b) 14 (c) 10 (d) 100
  15. 15.In which quadrant does the point (1, 1) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  16. 16.What is the midpoint of the line joining (4, 0) and (14, 8)? (a) (4, 9) (b) (5, 4) (c) (9, 4) (d) (18, 8)
  17. 17.What is the distance between the points (5, 7) and (29, 0)? (a) 31 (b) 26 (c) 25 (d) 625
  18. 18.What is the distance between the points (9, 8) and (14, 20)? (a) 17 (b) 13 (c) 169 (d) 14
  19. 19.What is the distance between the points (6, 9) and (18, 18)? (a) 225 (b) 16 (c) 21 (d) 15
  20. 20.What is the midpoint of the line joining (9, 10) and (13, 8)? (a) (22, 18) (b) (11, 9) (c) (2, 1) (d) (9, 11)
  21. 21.In which quadrant does the point (9, −8) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  22. 22.What is the midpoint of the line joining (9, 10) and (11, 4)? (a) (10, 7) (b) (7, 10) (c) (1, 3) (d) (20, 14)
  23. 23.What is the midpoint of the line joining (1, 3) and (7, 13)? (a) (8, 4) (b) (8, 16) (c) (3, 5) (d) (4, 8)
  24. 24.What is the midpoint of the line joining (3, 5) and (7, 15)? (a) (10, 5) (b) (5, 10) (c) (2, 5) (d) (10, 20)
  25. 25.What is the distance between the points (1, 13) and (4, 9)? (a) 6 (b) 5 (c) 7 (d) 25
  26. 26.In which quadrant does the point (−1, 3) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  27. 27.What is the distance between the points (7, 9) and (13, 17)? (a) 10 (b) 100 (c) 14 (d) 11
  28. 28.What is the midpoint of the line joining (10, 7) and (12, 13)? (a) (22, 20) (b) (11, 10) (c) (10, 11) (d) (1, 3)
  29. 29.In which quadrant does the point (8, −3) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  30. 30.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 17 (c) 13 (d) 169
  31. 31.What is the distance between the points (0, 2) and (3, 6)? (a) 5 (b) 25 (c) 7 (d) 6
  32. 32.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 10 (c) 100 (d) 14
  33. 33.What is the distance between the points (5, 2) and (12, 26)? (a) 25 (b) 31 (c) 625 (d) 26
  34. 34.What is the midpoint of the line joining (6, 15) and (16, 3)? (a) (9, 11) (b) (11, 9) (c) (22, 18) (d) (5, 6)
  35. 35.In which quadrant does the point (−3, 5) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  36. 36.What is the midpoint of the line joining (5, 4) and (7, 2)? (a) (12, 6) (b) (6, 3) (c) (3, 6) (d) (1, 1)
  37. 37.What is the distance between the points (7, 1) and (13, 9)? (a) 100 (b) 10 (c) 11 (d) 14
  38. 38.In which quadrant does the point (5, −6) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  39. 39.What is the distance between the points (1, 8) and (10, 20)? (a) 225 (b) 21 (c) 15 (d) 16
  40. 40.In which quadrant does the point (−2, 3) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant

Answer key

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

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