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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 139 · 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, 4) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  2. 2.In which quadrant does the point (4, −9) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  3. 3.What is the midpoint of the line joining (9, 12) and (11, 8)? (a) (11, 10) (b) (1, 2) (c) (10, 10) (d) (20, 20)
  4. 4.What is the distance between the points (2, 18) and (14, 2)? (a) 20 (b) 21 (c) 28 (d) 400
  5. 5.What is the distance between the points (8, 6) and (12, 9)? (a) 7 (b) 6 (c) 5 (d) 25
  6. 6.In which quadrant does the point (−6, −8) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  7. 7.What is the midpoint of the line joining (2, 9) and (6, 15)? (a) (4, 12) (b) (2, 3) (c) (12, 4) (d) (8, 24)
  8. 8.What is the midpoint of the line joining (1, 11) and (3, 3)? (a) (4, 14) (b) (2, 7) (c) (1, 4) (d) (7, 2)
  9. 9.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 21 (c) 400 (d) 28
  10. 10.How far is the point (12, 16) from the origin (0, 0)? (a) 20 (b) 28 (c) 400 (d) 21
  11. 11.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 15 (c) 21 (d) 16
  12. 12.In which quadrant does the point (−9, 5) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  13. 13.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 31 (c) 25 (d) 625
  14. 14.In which quadrant does the point (5, 5) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  15. 15.What is the midpoint of the line joining (0, 13) and (8, 9)? (a) (11, 4) (b) (4, 2) (c) (8, 22) (d) (4, 11)
  16. 16.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 11 (c) 10 (d) 100
  17. 17.What is the distance between the points (3, 19) and (12, 7)? (a) 225 (b) 15 (c) 21 (d) 16
  18. 18.What is the midpoint of the line joining (2, 8) and (6, 4)? (a) (6, 4) (b) (2, 2) (c) (4, 6) (d) (8, 12)
  19. 19.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 7 (c) 25 (d) 6
  20. 20.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 5 (c) 25 (d) 7
  21. 21.What is the distance between the points (4, 2) and (9, 14)? (a) 13 (b) 14 (c) 17 (d) 169
  22. 22.What is the distance between the points (6, 9) and (30, 2)? (a) 26 (b) 625 (c) 25 (d) 31
  23. 23.What is the distance between the points (3, 16) and (15, 0)? (a) 21 (b) 28 (c) 20 (d) 400
  24. 24.In which quadrant does the point (1, 4) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  25. 25.What is the distance between the points (9, 7) and (24, 15)? (a) 18 (b) 289 (c) 23 (d) 17
  26. 26.What is the distance between the points (7, 11) and (11, 8)? (a) 7 (b) 6 (c) 5 (d) 25
  27. 27.In which quadrant does the point (1, 6) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  28. 28.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 14 (c) 11 (d) 10
  29. 29.What is the midpoint of the line joining (6, 8) and (10, 6)? (a) (7, 8) (b) (8, 7) (c) (16, 14) (d) (2, 1)
  30. 30.What is the midpoint of the line joining (3, 2) and (9, 14)? (a) (6, 8) (b) (12, 16) (c) (3, 6) (d) (8, 6)
  31. 31.What is the midpoint of the line joining (9, 3) and (21, 11)? (a) (7, 15) (b) (15, 7) (c) (6, 4) (d) (30, 14)
  32. 32.In which quadrant does the point (9, −1) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  33. 33.In which quadrant does the point (−5, −5) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  34. 34.What is the distance between the points (2, 5) and (10, 11)? (a) 100 (b) 11 (c) 14 (d) 10
  35. 35.In which quadrant does the point (−4, 6) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  36. 36.What is the midpoint of the line joining (2, 3) and (4, 7)? (a) (3, 5) (b) (5, 3) (c) (6, 10) (d) (1, 2)
  37. 37.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 13 (c) 169 (d) 17
  38. 38.What is the distance between the points (3, 5) and (11, 11)? (a) 10 (b) 11 (c) 100 (d) 14
  39. 39.What is the midpoint of the line joining (1, 2) and (5, 0)? (a) (2, 1) (b) (1, 3) (c) (6, 2) (d) (3, 1)
  40. 40.What is the distance between the points (5, 6) and (8, 2)? (a) 6 (b) 5 (c) 25 (d) 7

Answer key

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

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