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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 556 · 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, 9) and (18, 4)? (a) 14 (b) 169 (c) 13 (d) 17
  2. 2.In which quadrant does the point (8, 4) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  3. 3.What is the distance between the points (8, 15) and (13, 3)? (a) 169 (b) 14 (c) 17 (d) 13
  4. 4.What is the midpoint of the line joining (0, 8) and (8, 18)? (a) (4, 5) (b) (8, 26) (c) (4, 13) (d) (13, 4)
  5. 5.What is the midpoint of the line joining (2, 6) and (6, 8)? (a) (8, 14) (b) (7, 4) (c) (2, 1) (d) (4, 7)
  6. 6.In which quadrant does the point (5, −7) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  7. 7.What is the midpoint of the line joining (4, 7) and (8, 5)? (a) (7, 6) (b) (12, 12) (c) (2, 1) (d) (6, 6)
  8. 8.What is the midpoint of the line joining (5, 5) and (17, 11)? (a) (11, 8) (b) (8, 11) (c) (22, 16) (d) (6, 3)
  9. 9.What is the distance between the points (3, 2) and (12, 14)? (a) 21 (b) 225 (c) 15 (d) 16
  10. 10.In which quadrant does the point (5, −9) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  11. 11.In which quadrant does the point (−6, −5) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  12. 12.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 18 (c) 289 (d) 23
  13. 13.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 23 (c) 17 (d) 18
  14. 14.In which quadrant does the point (7, 7) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  15. 15.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 21 (c) 20 (d) 28
  16. 16.In which quadrant does the point (−2, 2) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  17. 17.In which quadrant does the point (7, 4) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  18. 18.What is the distance between the points (4, 7) and (20, 19)? (a) 28 (b) 400 (c) 21 (d) 20
  19. 19.What is the distance between the points (8, 7) and (20, 2)? (a) 14 (b) 17 (c) 169 (d) 13
  20. 20.What is the midpoint of the line joining (8, 1) and (14, 3)? (a) (3, 1) (b) (11, 2) (c) (22, 4) (d) (2, 11)
  21. 21.What is the distance between the points (0, 2) and (6, 10)? (a) 11 (b) 10 (c) 14 (d) 100
  22. 22.What is the midpoint of the line joining (7, 11) and (17, 7)? (a) (12, 9) (b) (24, 18) (c) (9, 12) (d) (5, 2)
  23. 23.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 26 (c) 25 (d) 31
  24. 24.What is the distance between the points (7, 1) and (19, 10)? (a) 225 (b) 21 (c) 16 (d) 15
  25. 25.What is the midpoint of the line joining (4, 4) and (6, 8)? (a) (5, 6) (b) (6, 5) (c) (10, 12) (d) (1, 2)
  26. 26.What is the distance between the points (0, 15) and (24, 8)? (a) 625 (b) 26 (c) 31 (d) 25
  27. 27.What is the midpoint of the line joining (2, 14) and (4, 8)? (a) (6, 22) (b) (1, 3) (c) (11, 3) (d) (3, 11)
  28. 28.What is the distance between the points (7, 19) and (15, 4)? (a) 23 (b) 17 (c) 289 (d) 18
  29. 29.What is the midpoint of the line joining (5, 4) and (7, 14)? (a) (12, 18) (b) (1, 5) (c) (9, 6) (d) (6, 9)
  30. 30.What is the midpoint of the line joining (1, 9) and (9, 3)? (a) (10, 12) (b) (5, 6) (c) (6, 5) (d) (4, 3)
  31. 31.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 7 (c) 6 (d) 5
  32. 32.In which quadrant does the point (1, 3) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  33. 33.What is the distance between the points (1, 17) and (13, 1)? (a) 400 (b) 28 (c) 21 (d) 20
  34. 34.What is the distance between the points (0, 15) and (8, 0)? (a) 289 (b) 17 (c) 23 (d) 18
  35. 35.What is the distance between the points (4, 25) and (11, 1)? (a) 26 (b) 25 (c) 625 (d) 31
  36. 36.What is the distance between the points (9, 3) and (33, 10)? (a) 25 (b) 31 (c) 26 (d) 625
  37. 37.In which quadrant does the point (−5, −9) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  38. 38.What is the midpoint of the line joining (4, 5) and (8, 11)? (a) (6, 8) (b) (8, 6) (c) (12, 16) (d) (2, 3)
  39. 39.In which quadrant does the point (5, 9) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  40. 40.What is the distance between the points (2, 8) and (14, 3)? (a) 13 (b) 14 (c) 169 (d) 17

Answer key

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

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