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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 51 · 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, 19) and (11, 7)? (a) 169 (b) 14 (c) 17 (d) 13
  2. 2.In which quadrant does the point (−7, −4) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  3. 3.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 26 (c) 25 (d) 31
  4. 4.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 14 (c) 17 (d) 13
  5. 5.What is the midpoint of the line joining (0, 6) and (8, 18)? (a) (8, 24) (b) (4, 6) (c) (12, 4) (d) (4, 12)
  6. 6.What is the distance between the points (0, 5) and (15, 13)? (a) 289 (b) 18 (c) 23 (d) 17
  7. 7.In which quadrant does the point (1, 4) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  8. 8.What is the distance between the points (6, 10) and (18, 5)? (a) 17 (b) 169 (c) 13 (d) 14
  9. 9.What is the midpoint of the line joining (8, 8) and (16, 2)? (a) (5, 12) (b) (4, 3) (c) (24, 10) (d) (12, 5)
  10. 10.What is the distance between the points (2, 9) and (7, 21)? (a) 13 (b) 14 (c) 169 (d) 17
  11. 11.What is the distance between the points (1, 1) and (6, 13)? (a) 17 (b) 13 (c) 14 (d) 169
  12. 12.How far is the point (4, 3) from the origin (0, 0)? (a) 5 (b) 7 (c) 6 (d) 25
  13. 13.In which quadrant does the point (7, 8) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  14. 14.What is the midpoint of the line joining (6, 13) and (18, 1)? (a) (7, 12) (b) (24, 14) (c) (12, 7) (d) (6, 6)
  15. 15.What is the distance between the points (8, 17) and (16, 2)? (a) 18 (b) 23 (c) 17 (d) 289
  16. 16.What is the distance between the points (1, 6) and (17, 18)? (a) 400 (b) 20 (c) 28 (d) 21
  17. 17.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 11 (c) 14 (d) 100
  18. 18.What is the midpoint of the line joining (2, 1) and (8, 11)? (a) (5, 6) (b) (10, 12) (c) (3, 5) (d) (6, 5)
  19. 19.In which quadrant does the point (−1, 4) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  20. 20.In which quadrant does the point (−4, −1) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  21. 21.In which quadrant does the point (8, −5) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  22. 22.What is the midpoint of the line joining (3, 5) and (15, 13)? (a) (18, 18) (b) (9, 9) (c) (10, 9) (d) (6, 4)
  23. 23.What is the distance between the points (9, 16) and (15, 8)? (a) 100 (b) 14 (c) 10 (d) 11
  24. 24.What is the distance between the points (7, 10) and (31, 3)? (a) 26 (b) 625 (c) 31 (d) 25
  25. 25.What is the distance between the points (3, 11) and (6, 7)? (a) 5 (b) 25 (c) 6 (d) 7
  26. 26.What is the midpoint of the line joining (0, 16) and (2, 6)? (a) (11, 1) (b) (2, 22) (c) (1, 5) (d) (1, 11)
  27. 27.What is the distance between the points (4, 2) and (16, 11)? (a) 16 (b) 15 (c) 21 (d) 225
  28. 28.What is the midpoint of the line joining (1, 10) and (3, 12)? (a) (1, 1) (b) (2, 11) (c) (4, 22) (d) (11, 2)
  29. 29.What is the distance between the points (1, 16) and (25, 9)? (a) 625 (b) 25 (c) 26 (d) 31
  30. 30.In which quadrant does the point (−7, 4) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  31. 31.What is the distance between the points (0, 0) and (4, 3)? (a) 6 (b) 25 (c) 5 (d) 7
  32. 32.In which quadrant does the point (−9, −7) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  33. 33.What is the distance between the points (2, 1) and (17, 9)? (a) 289 (b) 17 (c) 23 (d) 18
  34. 34.What is the midpoint of the line joining (6, 1) and (18, 13)? (a) (6, 6) (b) (24, 14) (c) (7, 12) (d) (12, 7)
  35. 35.What is the distance between the points (4, 9) and (10, 1)? (a) 14 (b) 11 (c) 100 (d) 10
  36. 36.In which quadrant does the point (4, −7) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  37. 37.What is the midpoint of the line joining (0, 4) and (6, 6)? (a) (5, 3) (b) (3, 5) (c) (3, 1) (d) (6, 10)
  38. 38.In which quadrant does the point (1, −9) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  39. 39.In which quadrant does the point (−2, −4) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  40. 40.What is the distance between the points (4, 31) and (11, 7)? (a) 31 (b) 26 (c) 625 (d) 25

Answer key

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

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