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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 376 · 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 (1, 10) and (4, 6)? (a) 7 (b) 5 (c) 25 (d) 6
  2. 2.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 225 (c) 16 (d) 15
  3. 3.In which quadrant does the point (−3, −5) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  4. 4.What is the distance between the points (6, 2) and (15, 14)? (a) 21 (b) 16 (c) 225 (d) 15
  5. 5.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 14 (c) 13 (d) 17
  6. 6.In which quadrant does the point (4, 3) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  7. 7.In which quadrant does the point (5, 7) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  8. 8.What is the midpoint of the line joining (8, 12) and (10, 0)? (a) (6, 9) (b) (1, 6) (c) (18, 12) (d) (9, 6)
  9. 9.What is the distance between the points (2, 9) and (14, 0)? (a) 15 (b) 16 (c) 21 (d) 225
  10. 10.What is the midpoint of the line joining (1, 0) and (5, 6)? (a) (6, 6) (b) (4, 3) (c) (2, 3) (d) (3, 3)
  11. 11.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 21 (c) 225 (d) 15
  12. 12.What is the midpoint of the line joining (2, 0) and (14, 6)? (a) (6, 3) (b) (8, 3) (c) (3, 8) (d) (16, 6)
  13. 13.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 21 (c) 400 (d) 20
  14. 14.In which quadrant does the point (−8, 5) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  15. 15.What is the distance between the points (5, 10) and (11, 2)? (a) 100 (b) 11 (c) 14 (d) 10
  16. 16.In which quadrant does the point (−4, 6) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  17. 17.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 14 (c) 11 (d) 10
  18. 18.What is the distance between the points (7, 9) and (19, 18)? (a) 15 (b) 21 (c) 225 (d) 16
  19. 19.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 289 (c) 23 (d) 17
  20. 20.What is the distance between the points (5, 2) and (10, 14)? (a) 13 (b) 169 (c) 17 (d) 14
  21. 21.What is the midpoint of the line joining (2, 8) and (8, 12)? (a) (10, 20) (b) (10, 5) (c) (5, 10) (d) (3, 2)
  22. 22.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 6 (c) 5 (d) 25
  23. 23.In which quadrant does the point (3, 1) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  24. 24.What is the distance between the points (9, 2) and (21, 7)? (a) 17 (b) 14 (c) 13 (d) 169
  25. 25.What is the distance between the points (7, 19) and (12, 7)? (a) 13 (b) 14 (c) 169 (d) 17
  26. 26.What is the midpoint of the line joining (6, 6) and (18, 4)? (a) (6, 1) (b) (24, 10) (c) (12, 5) (d) (5, 12)
  27. 27.In which quadrant does the point (7, −1) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  28. 28.In which quadrant does the point (8, 9) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  29. 29.What is the distance between the points (9, 1) and (15, 9)? (a) 100 (b) 11 (c) 10 (d) 14
  30. 30.What is the distance between the points (7, 0) and (15, 6)? (a) 11 (b) 10 (c) 100 (d) 14
  31. 31.In which quadrant does the point (2, 3) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  32. 32.What is the midpoint of the line joining (9, 6) and (19, 4)? (a) (14, 5) (b) (28, 10) (c) (5, 1) (d) (5, 14)
  33. 33.What is the distance between the points (1, 0) and (17, 12)? (a) 400 (b) 28 (c) 20 (d) 21
  34. 34.What is the midpoint of the line joining (0, 2) and (4, 8)? (a) (2, 5) (b) (2, 3) (c) (5, 2) (d) (4, 10)
  35. 35.What is the midpoint of the line joining (1, 10) and (11, 18)? (a) (12, 28) (b) (14, 6) (c) (6, 14) (d) (5, 4)
  36. 36.What is the distance between the points (3, 15) and (12, 3)? (a) 15 (b) 16 (c) 225 (d) 21
  37. 37.What is the midpoint of the line joining (10, 9) and (12, 13)? (a) (11, 11) (b) (22, 22) (c) (1, 2) (d) (12, 11)
  38. 38.What is the distance between the points (3, 8) and (27, 1)? (a) 25 (b) 625 (c) 26 (d) 31
  39. 39.What is the distance between the points (7, 14) and (16, 2)? (a) 225 (b) 15 (c) 21 (d) 16
  40. 40.In which quadrant does the point (5, −1) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant

Answer key

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

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