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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 183 · 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 (6, 8) from the origin (0, 0)? (a) 11 (b) 10 (c) 100 (d) 14
  2. 2.What is the distance between the points (7, 7) and (19, 16)? (a) 225 (b) 21 (c) 15 (d) 16
  3. 3.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 10 (c) 11 (d) 14
  4. 4.In which quadrant does the point (−5, 3) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  5. 5.What is the midpoint of the line joining (9, 10) and (17, 14)? (a) (26, 24) (b) (4, 2) (c) (13, 12) (d) (12, 13)
  6. 6.How far is the point (9, 12) from the origin (0, 0)? (a) 15 (b) 16 (c) 225 (d) 21
  7. 7.What is the midpoint of the line joining (4, 5) and (14, 9)? (a) (18, 14) (b) (5, 2) (c) (9, 7) (d) (7, 9)
  8. 8.What is the distance between the points (5, 12) and (21, 0)? (a) 20 (b) 400 (c) 21 (d) 28
  9. 9.What is the distance between the points (1, 3) and (5, 0)? (a) 6 (b) 25 (c) 5 (d) 7
  10. 10.In which quadrant does the point (−9, 3) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  11. 11.In which quadrant does the point (7, 1) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  12. 12.What is the midpoint of the line joining (0, 17) and (10, 5)? (a) (10, 22) (b) (5, 6) (c) (11, 5) (d) (5, 11)
  13. 13.What is the midpoint of the line joining (6, 4) and (12, 12)? (a) (3, 4) (b) (18, 16) (c) (9, 8) (d) (8, 9)
  14. 14.In which quadrant does the point (5, −8) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  15. 15.What is the midpoint of the line joining (5, 3) and (15, 5)? (a) (5, 1) (b) (10, 4) (c) (4, 10) (d) (20, 8)
  16. 16.In which quadrant does the point (1, −8) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  17. 17.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 289 (c) 23 (d) 18
  18. 18.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 18 (c) 17 (d) 289
  19. 19.How far is the point (7, 24) from the origin (0, 0)? (a) 25 (b) 26 (c) 31 (d) 625
  20. 20.What is the distance between the points (3, 1) and (11, 7)? (a) 10 (b) 100 (c) 11 (d) 14
  21. 21.What is the midpoint of the line joining (1, 2) and (7, 10)? (a) (4, 6) (b) (8, 12) (c) (3, 4) (d) (6, 4)
  22. 22.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 17 (c) 14 (d) 13
  23. 23.What is the distance between the points (0, 8) and (3, 12)? (a) 7 (b) 5 (c) 6 (d) 25
  24. 24.In which quadrant does the point (−8, 6) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  25. 25.What is the midpoint of the line joining (4, 5) and (14, 3)? (a) (9, 4) (b) (18, 8) (c) (5, 1) (d) (4, 9)
  26. 26.In which quadrant does the point (−6, −4) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  27. 27.In which quadrant does the point (−7, −6) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  28. 28.What is the midpoint of the line joining (1, 8) and (13, 12)? (a) (7, 10) (b) (6, 2) (c) (14, 20) (d) (10, 7)
  29. 29.What is the distance between the points (8, 6) and (17, 18)? (a) 21 (b) 15 (c) 16 (d) 225
  30. 30.What is the distance between the points (5, 23) and (13, 8)? (a) 17 (b) 289 (c) 23 (d) 18
  31. 31.In which quadrant does the point (3, −7) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  32. 32.What is the midpoint of the line joining (0, 20) and (6, 10)? (a) (6, 30) (b) (15, 3) (c) (3, 5) (d) (3, 15)
  33. 33.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 14 (c) 13 (d) 169
  34. 34.What is the midpoint of the line joining (10, 6) and (18, 2)? (a) (4, 2) (b) (28, 8) (c) (4, 14) (d) (14, 4)
  35. 35.What is the midpoint of the line joining (4, 14) and (10, 2)? (a) (8, 7) (b) (3, 6) (c) (7, 8) (d) (14, 16)
  36. 36.What is the midpoint of the line joining (5, 1) and (15, 7)? (a) (5, 3) (b) (4, 10) (c) (20, 8) (d) (10, 4)
  37. 37.What is the midpoint of the line joining (1, 16) and (5, 6)? (a) (2, 5) (b) (6, 22) (c) (3, 11) (d) (11, 3)
  38. 38.What is the distance between the points (4, 2) and (12, 17)? (a) 17 (b) 289 (c) 23 (d) 18
  39. 39.What is the distance between the points (7, 9) and (11, 12)? (a) 25 (b) 7 (c) 5 (d) 6
  40. 40.What is the distance between the points (9, 0) and (33, 7)? (a) 625 (b) 26 (c) 25 (d) 31

Answer key

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

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