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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 243 · 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, 9) and (17, 14)? (a) 13 (b) 169 (c) 14 (d) 17
  2. 2.What is the distance between the points (6, 0) and (18, 9)? (a) 21 (b) 225 (c) 16 (d) 15
  3. 3.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 14 (c) 17 (d) 13
  4. 4.What is the midpoint of the line joining (4, 14) and (10, 8)? (a) (7, 11) (b) (11, 7) (c) (14, 22) (d) (3, 3)
  5. 5.What is the distance between the points (0, 2) and (9, 14)? (a) 15 (b) 16 (c) 225 (d) 21
  6. 6.In which quadrant does the point (−6, 8) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  7. 7.What is the midpoint of the line joining (6, 9) and (14, 21)? (a) (20, 30) (b) (4, 6) (c) (10, 15) (d) (15, 10)
  8. 8.What is the distance between the points (7, 15) and (22, 7)? (a) 23 (b) 17 (c) 18 (d) 289
  9. 9.What is the midpoint of the line joining (7, 8) and (9, 18)? (a) (13, 8) (b) (8, 13) (c) (16, 26) (d) (1, 5)
  10. 10.What is the distance between the points (7, 11) and (15, 5)? (a) 14 (b) 10 (c) 11 (d) 100
  11. 11.What is the distance between the points (0, 5) and (24, 12)? (a) 25 (b) 625 (c) 26 (d) 31
  12. 12.In which quadrant does the point (6, 5) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  13. 13.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 6 (c) 25 (d) 5
  14. 14.In which quadrant does the point (3, 8) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  15. 15.What is the distance between the points (1, 17) and (6, 5)? (a) 17 (b) 14 (c) 13 (d) 169
  16. 16.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 18 (c) 289 (d) 17
  17. 17.In which quadrant does the point (8, 1) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  18. 18.What is the midpoint of the line joining (7, 0) and (11, 8)? (a) (4, 9) (b) (2, 4) (c) (9, 4) (d) (18, 8)
  19. 19.What is the distance between the points (0, 16) and (8, 1)? (a) 23 (b) 289 (c) 17 (d) 18
  20. 20.What is the distance between the points (5, 1) and (12, 25)? (a) 25 (b) 31 (c) 625 (d) 26
  21. 21.In which quadrant does the point (−9, 8) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  22. 22.In which quadrant does the point (2, −7) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  23. 23.In which quadrant does the point (4, −8) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  24. 24.What is the distance between the points (2, 0) and (18, 12)? (a) 20 (b) 400 (c) 28 (d) 21
  25. 25.What is the distance between the points (0, 13) and (5, 1)? (a) 14 (b) 169 (c) 13 (d) 17
  26. 26.What is the distance between the points (8, 16) and (16, 1)? (a) 23 (b) 289 (c) 18 (d) 17
  27. 27.What is the distance between the points (8, 3) and (20, 8)? (a) 13 (b) 169 (c) 17 (d) 14
  28. 28.What is the midpoint of the line joining (9, 13) and (21, 3)? (a) (6, 5) (b) (15, 8) (c) (8, 15) (d) (30, 16)
  29. 29.What is the distance between the points (0, 5) and (3, 9)? (a) 25 (b) 6 (c) 7 (d) 5
  30. 30.What is the distance between the points (5, 16) and (13, 1)? (a) 17 (b) 289 (c) 23 (d) 18
  31. 31.What is the distance between the points (5, 17) and (21, 5)? (a) 21 (b) 20 (c) 400 (d) 28
  32. 32.What is the distance between the points (1, 1) and (25, 8)? (a) 625 (b) 25 (c) 31 (d) 26
  33. 33.What is the distance between the points (6, 7) and (9, 11)? (a) 25 (b) 6 (c) 7 (d) 5
  34. 34.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 7 (c) 5 (d) 25
  35. 35.In which quadrant does the point (9, −8) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  36. 36.In which quadrant does the point (4, 6) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  37. 37.What is the midpoint of the line joining (3, 4) and (5, 14)? (a) (9, 4) (b) (1, 5) (c) (4, 9) (d) (8, 18)
  38. 38.What is the midpoint of the line joining (5, 9) and (13, 5)? (a) (4, 2) (b) (18, 14) (c) (7, 9) (d) (9, 7)
  39. 39.What is the distance between the points (7, 13) and (31, 6)? (a) 26 (b) 625 (c) 25 (d) 31
  40. 40.In which quadrant does the point (−3, −7) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant

Answer key

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

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