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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 461 · 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 (9, −2) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  2. 2.What is the distance between the points (7, 18) and (19, 2)? (a) 21 (b) 28 (c) 400 (d) 20
  3. 3.What is the distance between the points (9, 5) and (14, 17)? (a) 169 (b) 13 (c) 14 (d) 17
  4. 4.What is the midpoint of the line joining (6, 8) and (18, 18)? (a) (13, 12) (b) (12, 13) (c) (24, 26) (d) (6, 5)
  5. 5.What is the midpoint of the line joining (9, 3) and (11, 15)? (a) (9, 10) (b) (20, 18) (c) (1, 6) (d) (10, 9)
  6. 6.What is the distance between the points (7, 21) and (16, 9)? (a) 21 (b) 225 (c) 15 (d) 16
  7. 7.What is the distance between the points (8, 9) and (32, 16)? (a) 25 (b) 31 (c) 26 (d) 625
  8. 8.What is the distance between the points (1, 5) and (17, 17)? (a) 28 (b) 400 (c) 20 (d) 21
  9. 9.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 20 (c) 28 (d) 400
  10. 10.What is the distance between the points (4, 3) and (7, 7)? (a) 6 (b) 25 (c) 5 (d) 7
  11. 11.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 14 (c) 100 (d) 11
  12. 12.What is the midpoint of the line joining (6, 1) and (8, 3)? (a) (1, 1) (b) (7, 2) (c) (14, 4) (d) (2, 7)
  13. 13.What is the midpoint of the line joining (4, 5) and (10, 7)? (a) (7, 6) (b) (14, 12) (c) (6, 7) (d) (3, 1)
  14. 14.What is the distance between the points (4, 7) and (13, 19)? (a) 21 (b) 225 (c) 16 (d) 15
  15. 15.What is the midpoint of the line joining (5, 8) and (15, 4)? (a) (6, 10) (b) (5, 2) (c) (10, 6) (d) (20, 12)
  16. 16.What is the distance between the points (8, 18) and (17, 6)? (a) 21 (b) 15 (c) 225 (d) 16
  17. 17.In which quadrant does the point (3, 4) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  18. 18.What is the distance between the points (6, 3) and (10, 0)? (a) 5 (b) 6 (c) 7 (d) 25
  19. 19.In which quadrant does the point (−8, 5) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  20. 20.In which quadrant does the point (2, −8) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  21. 21.What is the distance between the points (9, 9) and (15, 17)? (a) 11 (b) 10 (c) 14 (d) 100
  22. 22.What is the distance between the points (4, 0) and (16, 5)? (a) 17 (b) 169 (c) 14 (d) 13
  23. 23.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 5 (c) 7 (d) 25
  24. 24.In which quadrant does the point (−8, −8) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  25. 25.What is the distance between the points (5, 5) and (14, 17)? (a) 21 (b) 15 (c) 16 (d) 225
  26. 26.What is the midpoint of the line joining (9, 5) and (15, 1)? (a) (3, 2) (b) (12, 3) (c) (24, 6) (d) (3, 12)
  27. 27.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 100 (c) 14 (d) 11
  28. 28.What is the distance between the points (1, 0) and (13, 16)? (a) 28 (b) 21 (c) 400 (d) 20
  29. 29.In which quadrant does the point (9, −3) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  30. 30.What is the distance between the points (4, 0) and (8, 3)? (a) 25 (b) 5 (c) 6 (d) 7
  31. 31.In which quadrant does the point (−1, −3) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  32. 32.What is the distance between the points (1, 16) and (7, 8)? (a) 11 (b) 100 (c) 10 (d) 14
  33. 33.What is the distance between the points (6, 5) and (12, 13)? (a) 14 (b) 10 (c) 11 (d) 100
  34. 34.What is the distance between the points (4, 3) and (28, 10)? (a) 31 (b) 625 (c) 25 (d) 26
  35. 35.What is the distance between the points (5, 12) and (9, 9)? (a) 6 (b) 7 (c) 5 (d) 25
  36. 36.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 26 (c) 25 (d) 31
  37. 37.What is the midpoint of the line joining (10, 20) and (20, 8)? (a) (14, 15) (b) (30, 28) (c) (5, 6) (d) (15, 14)
  38. 38.What is the distance between the points (0, 21) and (12, 5)? (a) 28 (b) 21 (c) 400 (d) 20
  39. 39.In which quadrant does the point (−6, 1) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  40. 40.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 400 (c) 28 (d) 21

Answer key

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

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