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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 502 · 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, 0) and (9, 4)? (a) 25 (b) 5 (c) 7 (d) 6
  2. 2.What is the distance between the points (7, 15) and (19, 6)? (a) 16 (b) 15 (c) 225 (d) 21
  3. 3.What is the distance between the points (7, 4) and (10, 8)? (a) 5 (b) 25 (c) 7 (d) 6
  4. 4.What is the distance between the points (2, 1) and (5, 5)? (a) 6 (b) 25 (c) 5 (d) 7
  5. 5.In which quadrant does the point (−7, 3) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  6. 6.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 17 (c) 289 (d) 23
  7. 7.In which quadrant does the point (8, 1) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  8. 8.What is the distance between the points (5, 0) and (9, 3)? (a) 7 (b) 5 (c) 25 (d) 6
  9. 9.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 16 (c) 225 (d) 15
  10. 10.What is the distance between the points (2, 0) and (7, 12)? (a) 17 (b) 169 (c) 14 (d) 13
  11. 11.In which quadrant does the point (−8, 1) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  12. 12.In which quadrant does the point (7, 3) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  13. 13.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 400 (c) 20 (d) 21
  14. 14.What is the midpoint of the line joining (0, 10) and (8, 20)? (a) (8, 30) (b) (15, 4) (c) (4, 15) (d) (4, 5)
  15. 15.What is the distance between the points (1, 8) and (9, 23)? (a) 23 (b) 17 (c) 18 (d) 289
  16. 16.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 18 (c) 17 (d) 289
  17. 17.In which quadrant does the point (−9, −3) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  18. 18.What is the midpoint of the line joining (1, 8) and (9, 2)? (a) (6, 5) (b) (4, 3) (c) (10, 10) (d) (5, 5)
  19. 19.In which quadrant does the point (6, 3) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  20. 20.What is the distance between the points (0, 33) and (7, 9)? (a) 26 (b) 625 (c) 31 (d) 25
  21. 21.What is the distance between the points (0, 3) and (5, 15)? (a) 13 (b) 14 (c) 169 (d) 17
  22. 22.What is the distance between the points (0, 22) and (12, 6)? (a) 400 (b) 20 (c) 21 (d) 28
  23. 23.What is the midpoint of the line joining (10, 3) and (20, 9)? (a) (30, 12) (b) (15, 6) (c) (5, 3) (d) (6, 15)
  24. 24.In which quadrant does the point (7, 4) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  25. 25.In which quadrant does the point (5, 2) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  26. 26.In which quadrant does the point (−2, 1) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  27. 27.What is the distance between the points (3, 11) and (15, 6)? (a) 17 (b) 169 (c) 13 (d) 14
  28. 28.What is the distance between the points (8, 8) and (15, 32)? (a) 31 (b) 26 (c) 625 (d) 25
  29. 29.What is the midpoint of the line joining (8, 0) and (16, 2)? (a) (1, 12) (b) (4, 1) (c) (24, 2) (d) (12, 1)
  30. 30.In which quadrant does the point (3, 8) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  31. 31.In which quadrant does the point (−8, −3) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  32. 32.What is the midpoint of the line joining (10, 4) and (18, 12)? (a) (28, 16) (b) (8, 14) (c) (14, 8) (d) (4, 4)
  33. 33.What is the distance between the points (7, 7) and (19, 12)? (a) 17 (b) 169 (c) 14 (d) 13
  34. 34.What is the distance between the points (7, 16) and (19, 7)? (a) 225 (b) 21 (c) 16 (d) 15
  35. 35.What is the distance between the points (6, 12) and (12, 4)? (a) 11 (b) 10 (c) 100 (d) 14
  36. 36.What is the distance between the points (7, 6) and (12, 18)? (a) 13 (b) 14 (c) 17 (d) 169
  37. 37.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 25 (c) 5 (d) 7
  38. 38.What is the distance between the points (2, 17) and (14, 1)? (a) 21 (b) 400 (c) 20 (d) 28
  39. 39.In which quadrant does the point (−3, 2) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  40. 40.What is the midpoint of the line joining (10, 10) and (16, 2)? (a) (26, 12) (b) (3, 4) (c) (13, 6) (d) (6, 13)

Answer key

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

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