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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 654 · 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.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 11 (c) 10 (d) 14
  2. 2.What is the distance between the points (9, 4) and (14, 16)? (a) 17 (b) 14 (c) 169 (d) 13
  3. 3.In which quadrant does the point (1, 3) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  4. 4.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 15 (c) 16 (d) 21
  5. 5.What is the distance between the points (7, 17) and (19, 8)? (a) 16 (b) 225 (c) 15 (d) 21
  6. 6.In which quadrant does the point (3, 4) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  7. 7.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 20 (c) 21 (d) 400
  8. 8.What is the distance between the points (0, 8) and (6, 0)? (a) 100 (b) 11 (c) 10 (d) 14
  9. 9.What is the distance between the points (0, 18) and (16, 6)? (a) 28 (b) 20 (c) 400 (d) 21
  10. 10.What is the distance between the points (0, 27) and (7, 3)? (a) 625 (b) 31 (c) 26 (d) 25
  11. 11.What is the midpoint of the line joining (4, 1) and (16, 5)? (a) (3, 10) (b) (10, 3) (c) (6, 2) (d) (20, 6)
  12. 12.In which quadrant does the point (5, 7) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  13. 13.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 5 (c) 7 (d) 25
  14. 14.What is the midpoint of the line joining (2, 0) and (4, 8)? (a) (1, 4) (b) (4, 3) (c) (6, 8) (d) (3, 4)
  15. 15.What is the distance between the points (7, 25) and (14, 1)? (a) 31 (b) 625 (c) 25 (d) 26
  16. 16.In which quadrant does the point (2, 7) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  17. 17.What is the distance between the points (6, 2) and (9, 6)? (a) 7 (b) 25 (c) 6 (d) 5
  18. 18.In which quadrant does the point (−1, −1) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  19. 19.In which quadrant does the point (4, −4) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  20. 20.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 100 (c) 10 (d) 14
  21. 21.What is the distance between the points (8, 0) and (12, 3)? (a) 7 (b) 5 (c) 6 (d) 25
  22. 22.In which quadrant does the point (7, −1) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  23. 23.What is the midpoint of the line joining (4, 7) and (6, 19)? (a) (5, 13) (b) (13, 5) (c) (10, 26) (d) (1, 6)
  24. 24.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 28 (c) 21 (d) 20
  25. 25.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 6 (c) 25 (d) 5
  26. 26.What is the distance between the points (5, 3) and (12, 27)? (a) 31 (b) 625 (c) 25 (d) 26
  27. 27.In which quadrant does the point (3, 3) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  28. 28.In which quadrant does the point (4, −2) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  29. 29.What is the midpoint of the line joining (6, 3) and (10, 5)? (a) (2, 1) (b) (4, 8) (c) (8, 4) (d) (16, 8)
  30. 30.In which quadrant does the point (−6, −5) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  31. 31.In which quadrant does the point (−2, 8) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  32. 32.What is the distance between the points (3, 6) and (18, 14)? (a) 289 (b) 17 (c) 23 (d) 18
  33. 33.What is the midpoint of the line joining (5, 2) and (15, 6)? (a) (5, 2) (b) (20, 8) (c) (10, 4) (d) (4, 10)
  34. 34.What is the midpoint of the line joining (2, 4) and (14, 12)? (a) (9, 8) (b) (16, 16) (c) (6, 4) (d) (8, 8)
  35. 35.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 17 (c) 23 (d) 18
  36. 36.In which quadrant does the point (6, 2) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  37. 37.What is the midpoint of the line joining (10, 6) and (12, 10)? (a) (8, 11) (b) (1, 2) (c) (22, 16) (d) (11, 8)
  38. 38.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 25 (c) 625 (d) 26
  39. 39.What is the midpoint of the line joining (1, 8) and (5, 14)? (a) (3, 11) (b) (2, 3) (c) (6, 22) (d) (11, 3)
  40. 40.What is the midpoint of the line joining (5, 0) and (13, 6)? (a) (18, 6) (b) (9, 3) (c) (4, 3) (d) (3, 9)

Answer key

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

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