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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 471 · 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 (4, −3) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  2. 2.What is the midpoint of the line joining (2, 6) and (8, 10)? (a) (3, 2) (b) (5, 8) (c) (10, 16) (d) (8, 5)
  3. 3.What is the distance between the points (5, 13) and (14, 1)? (a) 21 (b) 225 (c) 16 (d) 15
  4. 4.What is the distance between the points (2, 6) and (7, 18)? (a) 17 (b) 169 (c) 13 (d) 14
  5. 5.What is the midpoint of the line joining (8, 1) and (14, 5)? (a) (11, 3) (b) (22, 6) (c) (3, 2) (d) (3, 11)
  6. 6.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 23 (c) 289 (d) 17
  7. 7.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 11 (c) 100 (d) 10
  8. 8.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 25 (c) 6 (d) 5
  9. 9.In which quadrant does the point (2, 2) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  10. 10.In which quadrant does the point (3, 6) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  11. 11.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 16 (c) 21 (d) 15
  12. 12.In which quadrant does the point (−6, 2) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  13. 13.In which quadrant does the point (−5, −8) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  14. 14.What is the midpoint of the line joining (9, 12) and (19, 10)? (a) (5, 1) (b) (11, 14) (c) (14, 11) (d) (28, 22)
  15. 15.What is the distance between the points (6, 16) and (22, 4)? (a) 28 (b) 21 (c) 20 (d) 400
  16. 16.In which quadrant does the point (−4, −6) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  17. 17.What is the distance between the points (4, 10) and (16, 5)? (a) 17 (b) 169 (c) 13 (d) 14
  18. 18.In which quadrant does the point (5, −3) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  19. 19.What is the distance between the points (2, 3) and (11, 15)? (a) 225 (b) 15 (c) 21 (d) 16
  20. 20.What is the distance between the points (5, 17) and (21, 5)? (a) 20 (b) 400 (c) 21 (d) 28
  21. 21.What is the midpoint of the line joining (10, 6) and (20, 4)? (a) (15, 5) (b) (30, 10) (c) (5, 1) (d) (5, 15)
  22. 22.How far is the point (4, 3) from the origin (0, 0)? (a) 5 (b) 25 (c) 7 (d) 6
  23. 23.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 17 (c) 23 (d) 18
  24. 24.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 625 (c) 31 (d) 25
  25. 25.What is the midpoint of the line joining (9, 11) and (11, 1)? (a) (6, 10) (b) (10, 6) (c) (20, 12) (d) (1, 5)
  26. 26.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 225 (c) 16 (d) 15
  27. 27.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 21 (c) 20 (d) 28
  28. 28.In which quadrant does the point (3, 3) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  29. 29.In which quadrant does the point (7, 8) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  30. 30.In which quadrant does the point (−8, 1) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  31. 31.What is the distance between the points (0, 0) and (16, 12)? (a) 400 (b) 21 (c) 20 (d) 28
  32. 32.In which quadrant does the point (9, 5) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  33. 33.What is the distance between the points (7, 3) and (11, 6)? (a) 6 (b) 7 (c) 5 (d) 25
  34. 34.What is the distance between the points (7, 5) and (19, 21)? (a) 28 (b) 400 (c) 20 (d) 21
  35. 35.What is the distance between the points (2, 10) and (14, 1)? (a) 15 (b) 225 (c) 16 (d) 21
  36. 36.What is the midpoint of the line joining (0, 8) and (10, 16)? (a) (12, 5) (b) (5, 12) (c) (10, 24) (d) (5, 4)
  37. 37.What is the midpoint of the line joining (8, 1) and (20, 13)? (a) (28, 14) (b) (14, 7) (c) (6, 6) (d) (7, 14)
  38. 38.What is the distance between the points (8, 15) and (13, 3)? (a) 17 (b) 14 (c) 169 (d) 13
  39. 39.What is the midpoint of the line joining (0, 9) and (4, 21)? (a) (4, 30) (b) (15, 2) (c) (2, 15) (d) (2, 6)
  40. 40.What is the distance between the points (1, 5) and (7, 13)? (a) 14 (b) 11 (c) 10 (d) 100

Answer key

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

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