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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 393 · 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.What is the distance between the points (6, 0) and (11, 12)? (a) 169 (b) 14 (c) 17 (d) 13
  2. 2.What is the distance between the points (6, 1) and (18, 10)? (a) 21 (b) 225 (c) 16 (d) 15
  3. 3.What is the distance between the points (8, 7) and (14, 15)? (a) 100 (b) 11 (c) 14 (d) 10
  4. 4.What is the distance between the points (7, 21) and (23, 9)? (a) 400 (b) 28 (c) 21 (d) 20
  5. 5.In which quadrant does the point (9, 1) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  6. 6.What is the distance between the points (8, 1) and (23, 9)? (a) 23 (b) 18 (c) 289 (d) 17
  7. 7.What is the midpoint of the line joining (8, 0) and (20, 4)? (a) (28, 4) (b) (6, 2) (c) (14, 2) (d) (2, 14)
  8. 8.What is the midpoint of the line joining (2, 6) and (4, 0)? (a) (4, 3) (b) (1, 3) (c) (3, 3) (d) (6, 6)
  9. 9.In which quadrant does the point (−7, 2) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  10. 10.In which quadrant does the point (7, 1) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  11. 11.In which quadrant does the point (6, 5) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  12. 12.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 169 (c) 17 (d) 13
  13. 13.In which quadrant does the point (6, −8) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  14. 14.What is the midpoint of the line joining (2, 4) and (8, 0)? (a) (3, 2) (b) (5, 2) (c) (10, 4) (d) (2, 5)
  15. 15.What is the distance between the points (9, 10) and (24, 2)? (a) 18 (b) 17 (c) 289 (d) 23
  16. 16.What is the distance between the points (7, 2) and (19, 18)? (a) 21 (b) 20 (c) 400 (d) 28
  17. 17.In which quadrant does the point (8, 2) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  18. 18.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 17 (c) 289 (d) 23
  19. 19.What is the midpoint of the line joining (4, 4) and (10, 0)? (a) (2, 7) (b) (14, 4) (c) (7, 2) (d) (3, 2)
  20. 20.What is the distance between the points (3, 7) and (27, 14)? (a) 625 (b) 26 (c) 25 (d) 31
  21. 21.What is the midpoint of the line joining (6, 17) and (10, 9)? (a) (16, 26) (b) (13, 8) (c) (8, 13) (d) (2, 4)
  22. 22.What is the distance between the points (8, 18) and (16, 3)? (a) 17 (b) 18 (c) 289 (d) 23
  23. 23.What is the distance between the points (0, 9) and (8, 3)? (a) 11 (b) 100 (c) 14 (d) 10
  24. 24.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 25 (c) 5 (d) 7
  25. 25.What is the midpoint of the line joining (3, 2) and (7, 8)? (a) (2, 3) (b) (5, 5) (c) (10, 10) (d) (6, 5)
  26. 26.In which quadrant does the point (−4, 6) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  27. 27.How far is the point (15, 8) from the origin (0, 0)? (a) 17 (b) 18 (c) 289 (d) 23
  28. 28.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 13 (c) 17 (d) 14
  29. 29.What is the midpoint of the line joining (3, 12) and (7, 0)? (a) (6, 5) (b) (10, 12) (c) (5, 6) (d) (2, 6)
  30. 30.In which quadrant does the point (6, −5) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  31. 31.How far is the point (16, 12) from the origin (0, 0)? (a) 400 (b) 28 (c) 21 (d) 20
  32. 32.In which quadrant does the point (3, −4) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  33. 33.What is the midpoint of the line joining (10, 7) and (16, 19)? (a) (3, 6) (b) (26, 26) (c) (14, 13) (d) (13, 13)
  34. 34.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 31 (c) 26 (d) 25
  35. 35.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 21 (c) 20 (d) 400
  36. 36.What is the distance between the points (2, 8) and (17, 0)? (a) 289 (b) 18 (c) 17 (d) 23
  37. 37.What is the midpoint of the line joining (0, 2) and (2, 4)? (a) (1, 1) (b) (3, 1) (c) (1, 3) (d) (2, 6)
  38. 38.What is the distance between the points (5, 4) and (17, 13)? (a) 15 (b) 225 (c) 21 (d) 16
  39. 39.What is the midpoint of the line joining (10, 13) and (20, 1)? (a) (5, 6) (b) (7, 15) (c) (30, 14) (d) (15, 7)
  40. 40.What is the distance between the points (7, 2) and (15, 8)? (a) 11 (b) 100 (c) 14 (d) 10

Answer key

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

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