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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 673 · 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 (5, 6) and (20, 14)? (a) 289 (b) 18 (c) 17 (d) 23
  2. 2.What is the distance between the points (9, 15) and (15, 7)? (a) 10 (b) 100 (c) 11 (d) 14
  3. 3.What is the distance between the points (8, 0) and (16, 15)? (a) 23 (b) 289 (c) 17 (d) 18
  4. 4.In which quadrant does the point (−9, 2) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  5. 5.What is the distance between the points (3, 8) and (27, 1)? (a) 31 (b) 26 (c) 625 (d) 25
  6. 6.In which quadrant does the point (−4, 4) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  7. 7.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 13 (c) 17 (d) 169
  8. 8.What is the midpoint of the line joining (8, 14) and (20, 8)? (a) (6, 3) (b) (11, 14) (c) (28, 22) (d) (14, 11)
  9. 9.In which quadrant does the point (4, −9) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  10. 10.In which quadrant does the point (−9, −6) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  11. 11.What is the distance between the points (4, 8) and (8, 11)? (a) 25 (b) 7 (c) 5 (d) 6
  12. 12.What is the midpoint of the line joining (0, 8) and (12, 6)? (a) (7, 6) (b) (6, 1) (c) (6, 7) (d) (12, 14)
  13. 13.In which quadrant does the point (−3, −7) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  14. 14.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 23 (c) 18 (d) 17
  15. 15.What is the distance between the points (2, 8) and (10, 2)? (a) 100 (b) 11 (c) 10 (d) 14
  16. 16.In which quadrant does the point (−2, −8) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  17. 17.What is the distance between the points (6, 7) and (9, 11)? (a) 5 (b) 6 (c) 25 (d) 7
  18. 18.What is the midpoint of the line joining (7, 10) and (9, 22)? (a) (16, 8) (b) (1, 6) (c) (16, 32) (d) (8, 16)
  19. 19.What is the distance between the points (0, 8) and (16, 20)? (a) 21 (b) 28 (c) 20 (d) 400
  20. 20.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 16 (c) 15 (d) 225
  21. 21.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 100 (c) 10 (d) 11
  22. 22.What is the midpoint of the line joining (6, 0) and (14, 8)? (a) (10, 4) (b) (4, 10) (c) (4, 4) (d) (20, 8)
  23. 23.In which quadrant does the point (5, 2) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  24. 24.What is the distance between the points (6, 3) and (12, 11)? (a) 14 (b) 10 (c) 100 (d) 11
  25. 25.What is the distance between the points (8, 7) and (11, 11)? (a) 5 (b) 7 (c) 6 (d) 25
  26. 26.What is the distance between the points (2, 7) and (5, 3)? (a) 25 (b) 6 (c) 7 (d) 5
  27. 27.What is the distance between the points (0, 12) and (6, 4)? (a) 11 (b) 10 (c) 14 (d) 100
  28. 28.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 16 (c) 15 (d) 225
  29. 29.What is the midpoint of the line joining (3, 9) and (7, 13)? (a) (2, 2) (b) (10, 22) (c) (11, 5) (d) (5, 11)
  30. 30.What is the distance between the points (5, 19) and (17, 3)? (a) 20 (b) 400 (c) 28 (d) 21
  31. 31.In which quadrant does the point (−1, −8) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  32. 32.What is the distance between the points (9, 21) and (25, 9)? (a) 28 (b) 21 (c) 400 (d) 20
  33. 33.What is the distance between the points (7, 10) and (13, 2)? (a) 14 (b) 10 (c) 100 (d) 11
  34. 34.What is the distance between the points (5, 1) and (13, 7)? (a) 10 (b) 14 (c) 100 (d) 11
  35. 35.In which quadrant does the point (−7, 4) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  36. 36.What is the distance between the points (1, 8) and (4, 12)? (a) 25 (b) 7 (c) 5 (d) 6
  37. 37.What is the distance between the points (3, 21) and (8, 9)? (a) 169 (b) 14 (c) 13 (d) 17
  38. 38.What is the distance between the points (0, 16) and (12, 0)? (a) 400 (b) 21 (c) 28 (d) 20
  39. 39.What is the distance between the points (8, 9) and (15, 33)? (a) 25 (b) 31 (c) 26 (d) 625
  40. 40.In which quadrant does the point (−8, 2) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant

Answer key

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

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