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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 172 · 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 (1, 9) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  2. 2.In which quadrant does the point (3, −6) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  3. 3.In which quadrant does the point (8, −4) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  4. 4.What is the midpoint of the line joining (2, 10) and (12, 12)? (a) (7, 11) (b) (14, 22) (c) (11, 7) (d) (5, 1)
  5. 5.What is the distance between the points (0, 9) and (12, 25)? (a) 20 (b) 28 (c) 21 (d) 400
  6. 6.In which quadrant does the point (−4, 5) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  7. 7.What is the distance between the points (1, 6) and (9, 0)? (a) 14 (b) 11 (c) 10 (d) 100
  8. 8.What is the distance between the points (2, 11) and (26, 4)? (a) 26 (b) 31 (c) 25 (d) 625
  9. 9.What is the midpoint of the line joining (2, 8) and (10, 12)? (a) (12, 20) (b) (10, 6) (c) (6, 10) (d) (4, 2)
  10. 10.What is the distance between the points (0, 3) and (16, 15)? (a) 28 (b) 20 (c) 21 (d) 400
  11. 11.What is the distance between the points (0, 17) and (6, 9)? (a) 14 (b) 100 (c) 10 (d) 11
  12. 12.How far is the point (12, 9) from the origin (0, 0)? (a) 16 (b) 225 (c) 21 (d) 15
  13. 13.What is the distance between the points (1, 0) and (4, 4)? (a) 7 (b) 6 (c) 5 (d) 25
  14. 14.What is the midpoint of the line joining (2, 8) and (6, 0)? (a) (8, 8) (b) (5, 4) (c) (4, 4) (d) (2, 4)
  15. 15.What is the distance between the points (6, 2) and (22, 14)? (a) 21 (b) 28 (c) 20 (d) 400
  16. 16.What is the distance between the points (6, 17) and (15, 5)? (a) 16 (b) 15 (c) 225 (d) 21
  17. 17.What is the distance between the points (9, 7) and (18, 19)? (a) 21 (b) 15 (c) 16 (d) 225
  18. 18.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 25 (c) 6 (d) 5
  19. 19.What is the distance between the points (2, 6) and (14, 22)? (a) 400 (b) 21 (c) 28 (d) 20
  20. 20.What is the distance between the points (5, 33) and (12, 9)? (a) 625 (b) 26 (c) 25 (d) 31
  21. 21.In which quadrant does the point (−2, −4) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  22. 22.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 13 (c) 17 (d) 14
  23. 23.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 7 (c) 25 (d) 5
  24. 24.What is the distance between the points (2, 5) and (14, 0)? (a) 14 (b) 17 (c) 13 (d) 169
  25. 25.What is the midpoint of the line joining (2, 10) and (12, 0)? (a) (5, 7) (b) (14, 10) (c) (5, 5) (d) (7, 5)
  26. 26.What is the distance between the points (2, 14) and (8, 6)? (a) 14 (b) 100 (c) 10 (d) 11
  27. 27.What is the distance between the points (7, 0) and (12, 12)? (a) 13 (b) 17 (c) 169 (d) 14
  28. 28.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 11 (c) 10 (d) 14
  29. 29.What is the distance between the points (9, 11) and (33, 4)? (a) 31 (b) 625 (c) 26 (d) 25
  30. 30.What is the midpoint of the line joining (3, 5) and (11, 17)? (a) (14, 22) (b) (11, 7) (c) (7, 11) (d) (4, 6)
  31. 31.What is the distance between the points (7, 7) and (19, 16)? (a) 15 (b) 225 (c) 21 (d) 16
  32. 32.How far is the point (12, 16) from the origin (0, 0)? (a) 20 (b) 400 (c) 21 (d) 28
  33. 33.In which quadrant does the point (2, −7) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  34. 34.What is the midpoint of the line joining (6, 10) and (8, 8)? (a) (1, 1) (b) (7, 9) (c) (14, 18) (d) (9, 7)
  35. 35.What is the distance between the points (5, 4) and (8, 8)? (a) 7 (b) 25 (c) 6 (d) 5
  36. 36.In which quadrant does the point (−7, 5) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  37. 37.What is the midpoint of the line joining (5, 9) and (17, 13)? (a) (12, 11) (b) (22, 22) (c) (6, 2) (d) (11, 11)
  38. 38.What is the distance between the points (2, 5) and (6, 8)? (a) 5 (b) 7 (c) 6 (d) 25
  39. 39.In which quadrant does the point (3, −1) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  40. 40.What is the distance between the points (6, 6) and (22, 18)? (a) 20 (b) 21 (c) 400 (d) 28

Answer key

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

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