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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 199 · 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) 10 (b) 11 (c) 100 (d) 14
  2. 2.In which quadrant does the point (−2, −2) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  3. 3.What is the distance between the points (5, 12) and (10, 0)? (a) 17 (b) 14 (c) 169 (d) 13
  4. 4.What is the midpoint of the line joining (10, 11) and (12, 1)? (a) (11, 6) (b) (22, 12) (c) (6, 11) (d) (1, 5)
  5. 5.In which quadrant does the point (−5, −7) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  6. 6.What is the distance between the points (9, 6) and (12, 2)? (a) 6 (b) 25 (c) 7 (d) 5
  7. 7.What is the distance between the points (6, 0) and (10, 3)? (a) 5 (b) 6 (c) 7 (d) 25
  8. 8.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 169 (c) 13 (d) 14
  9. 9.What is the distance between the points (7, 18) and (15, 3)? (a) 23 (b) 289 (c) 18 (d) 17
  10. 10.What is the distance between the points (8, 8) and (20, 13)? (a) 13 (b) 14 (c) 169 (d) 17
  11. 11.What is the midpoint of the line joining (10, 16) and (16, 8)? (a) (3, 4) (b) (26, 24) (c) (13, 12) (d) (12, 13)
  12. 12.In which quadrant does the point (−9, 3) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  13. 13.What is the midpoint of the line joining (8, 4) and (10, 12)? (a) (1, 4) (b) (8, 9) (c) (18, 16) (d) (9, 8)
  14. 14.In which quadrant does the point (3, 5) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  15. 15.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 13 (c) 17 (d) 14
  16. 16.What is the distance between the points (6, 3) and (12, 11)? (a) 10 (b) 100 (c) 14 (d) 11
  17. 17.What is the distance between the points (5, 6) and (8, 10)? (a) 25 (b) 6 (c) 5 (d) 7
  18. 18.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 17 (c) 289 (d) 23
  19. 19.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 7 (c) 6 (d) 25
  20. 20.In which quadrant does the point (−6, −7) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  21. 21.In which quadrant does the point (−3, 1) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  22. 22.What is the distance between the points (1, 17) and (17, 5)? (a) 400 (b) 28 (c) 20 (d) 21
  23. 23.In which quadrant does the point (2, −1) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  24. 24.In which quadrant does the point (9, −7) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  25. 25.What is the midpoint of the line joining (5, 2) and (9, 4)? (a) (14, 6) (b) (2, 1) (c) (7, 3) (d) (3, 7)
  26. 26.What is the midpoint of the line joining (4, 5) and (16, 3)? (a) (6, 1) (b) (4, 10) (c) (20, 8) (d) (10, 4)
  27. 27.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 21 (c) 20 (d) 400
  28. 28.What is the distance between the points (7, 14) and (31, 7)? (a) 26 (b) 31 (c) 25 (d) 625
  29. 29.What is the distance between the points (5, 32) and (12, 8)? (a) 31 (b) 26 (c) 25 (d) 625
  30. 30.What is the distance between the points (9, 3) and (33, 10)? (a) 26 (b) 625 (c) 31 (d) 25
  31. 31.In which quadrant does the point (−3, 5) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  32. 32.What is the midpoint of the line joining (2, 10) and (6, 18)? (a) (2, 4) (b) (14, 4) (c) (8, 28) (d) (4, 14)
  33. 33.What is the distance between the points (0, 12) and (12, 3)? (a) 16 (b) 15 (c) 21 (d) 225
  34. 34.In which quadrant does the point (−2, −6) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  35. 35.What is the distance between the points (5, 6) and (13, 12)? (a) 100 (b) 10 (c) 11 (d) 14
  36. 36.What is the distance between the points (6, 8) and (10, 11)? (a) 25 (b) 5 (c) 7 (d) 6
  37. 37.What is the midpoint of the line joining (10, 6) and (14, 10)? (a) (24, 16) (b) (12, 8) (c) (8, 12) (d) (2, 2)
  38. 38.In which quadrant does the point (−6, −6) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  39. 39.What is the midpoint of the line joining (6, 9) and (10, 15)? (a) (8, 12) (b) (12, 8) (c) (2, 3) (d) (16, 24)
  40. 40.What is the distance between the points (9, 10) and (15, 2)? (a) 11 (b) 100 (c) 10 (d) 14

Answer key

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

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