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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 141 · 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 (5, −3) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  2. 2.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 13 (c) 17 (d) 169
  3. 3.What is the distance between the points (4, 2) and (20, 14)? (a) 28 (b) 21 (c) 400 (d) 20
  4. 4.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 10 (c) 11 (d) 14
  5. 5.What is the midpoint of the line joining (7, 5) and (9, 17)? (a) (11, 8) (b) (8, 11) (c) (16, 22) (d) (1, 6)
  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 (0, 4) and (4, 7)? (a) 7 (b) 5 (c) 25 (d) 6
  8. 8.What is the midpoint of the line joining (9, 4) and (11, 14)? (a) (1, 5) (b) (10, 9) (c) (20, 18) (d) (9, 10)
  9. 9.What is the distance between the points (6, 0) and (21, 8)? (a) 289 (b) 18 (c) 23 (d) 17
  10. 10.What is the distance between the points (1, 6) and (7, 14)? (a) 11 (b) 14 (c) 10 (d) 100
  11. 11.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 6 (c) 5 (d) 25
  12. 12.What is the midpoint of the line joining (0, 0) and (8, 12)? (a) (4, 6) (b) (5, 6) (c) (8, 12) (d) (6, 4)
  13. 13.What is the midpoint of the line joining (10, 5) and (20, 7)? (a) (6, 15) (b) (5, 1) (c) (30, 12) (d) (15, 6)
  14. 14.In which quadrant does the point (−6, 6) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  15. 15.How far is the point (7, 24) from the origin (0, 0)? (a) 25 (b) 31 (c) 625 (d) 26
  16. 16.What is the distance between the points (1, 12) and (13, 3)? (a) 16 (b) 15 (c) 21 (d) 225
  17. 17.In which quadrant does the point (3, −1) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  18. 18.What is the distance between the points (1, 20) and (6, 8)? (a) 14 (b) 169 (c) 17 (d) 13
  19. 19.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 169 (c) 13 (d) 14
  20. 20.In which quadrant does the point (−3, 9) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  21. 21.In which quadrant does the point (−9, 4) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  22. 22.In which quadrant does the point (−7, −6) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  23. 23.In which quadrant does the point (−8, −3) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  24. 24.What is the midpoint of the line joining (3, 0) and (5, 12)? (a) (1, 6) (b) (8, 12) (c) (4, 6) (d) (6, 4)
  25. 25.What is the midpoint of the line joining (9, 3) and (19, 9)? (a) (6, 14) (b) (14, 6) (c) (5, 3) (d) (28, 12)
  26. 26.What is the distance between the points (9, 29) and (16, 5)? (a) 625 (b) 25 (c) 26 (d) 31
  27. 27.What is the midpoint of the line joining (5, 4) and (13, 0)? (a) (4, 2) (b) (9, 2) (c) (18, 4) (d) (2, 9)
  28. 28.What is the distance between the points (7, 3) and (11, 6)? (a) 7 (b) 5 (c) 6 (d) 25
  29. 29.What is the distance between the points (5, 14) and (11, 6)? (a) 14 (b) 100 (c) 11 (d) 10
  30. 30.What is the distance between the points (1, 9) and (13, 25)? (a) 28 (b) 21 (c) 400 (d) 20
  31. 31.What is the midpoint of the line joining (1, 4) and (5, 2)? (a) (2, 1) (b) (3, 3) (c) (6, 6) (d) (4, 3)
  32. 32.What is the midpoint of the line joining (8, 9) and (16, 15)? (a) (4, 3) (b) (13, 12) (c) (24, 24) (d) (12, 12)
  33. 33.What is the midpoint of the line joining (0, 4) and (10, 16)? (a) (5, 10) (b) (10, 5) (c) (10, 20) (d) (5, 6)
  34. 34.How far is the point (12, 9) from the origin (0, 0)? (a) 15 (b) 21 (c) 16 (d) 225
  35. 35.What is the midpoint of the line joining (9, 6) and (19, 18)? (a) (12, 14) (b) (5, 6) (c) (14, 12) (d) (28, 24)
  36. 36.In which quadrant does the point (−4, 8) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  37. 37.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 10 (c) 11 (d) 100
  38. 38.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 289 (c) 17 (d) 18
  39. 39.What is the midpoint of the line joining (9, 12) and (11, 6)? (a) (1, 3) (b) (9, 10) (c) (20, 18) (d) (10, 9)
  40. 40.What is the midpoint of the line joining (8, 5) and (16, 1)? (a) (3, 12) (b) (24, 6) (c) (12, 3) (d) (4, 2)

Answer key

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

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