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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 674 · 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 midpoint of the line joining (3, 6) and (5, 8)? (a) (1, 1) (b) (8, 14) (c) (7, 4) (d) (4, 7)
  2. 2.What is the distance between the points (3, 16) and (12, 4)? (a) 15 (b) 21 (c) 16 (d) 225
  3. 3.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 11 (c) 10 (d) 100
  4. 4.In which quadrant does the point (8, −2) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  5. 5.In which quadrant does the point (4, 3) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  6. 6.What is the distance between the points (2, 30) and (9, 6)? (a) 625 (b) 31 (c) 26 (d) 25
  7. 7.What is the midpoint of the line joining (1, 13) and (13, 1)? (a) (6, 6) (b) (8, 7) (c) (14, 14) (d) (7, 7)
  8. 8.In which quadrant does the point (−6, 8) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  9. 9.What is the distance between the points (6, 15) and (21, 7)? (a) 23 (b) 289 (c) 18 (d) 17
  10. 10.In which quadrant does the point (3, 7) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  11. 11.What is the midpoint of the line joining (4, 1) and (10, 11)? (a) (14, 12) (b) (6, 7) (c) (7, 6) (d) (3, 5)
  12. 12.What is the distance between the points (9, 9) and (24, 17)? (a) 18 (b) 23 (c) 289 (d) 17
  13. 13.In which quadrant does the point (−3, 2) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  14. 14.What is the distance between the points (9, 0) and (21, 5)? (a) 13 (b) 14 (c) 169 (d) 17
  15. 15.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 23 (c) 289 (d) 17
  16. 16.What is the distance between the points (4, 15) and (19, 7)? (a) 18 (b) 23 (c) 289 (d) 17
  17. 17.What is the midpoint of the line joining (7, 0) and (19, 10)? (a) (13, 5) (b) (5, 13) (c) (6, 5) (d) (26, 10)
  18. 18.What is the midpoint of the line joining (6, 18) and (18, 8)? (a) (12, 13) (b) (6, 5) (c) (24, 26) (d) (13, 12)
  19. 19.In which quadrant does the point (6, 7) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  20. 20.What is the midpoint of the line joining (0, 9) and (2, 21)? (a) (15, 1) (b) (2, 30) (c) (1, 6) (d) (1, 15)
  21. 21.What is the midpoint of the line joining (6, 2) and (18, 4)? (a) (24, 6) (b) (12, 3) (c) (3, 12) (d) (6, 1)
  22. 22.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 10 (c) 100 (d) 14
  23. 23.What is the midpoint of the line joining (5, 1) and (9, 13)? (a) (14, 14) (b) (8, 7) (c) (7, 7) (d) (2, 6)
  24. 24.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 6 (c) 25 (d) 7
  25. 25.What is the distance between the points (7, 6) and (15, 21)? (a) 17 (b) 289 (c) 18 (d) 23
  26. 26.What is the midpoint of the line joining (0, 4) and (12, 2)? (a) (3, 6) (b) (6, 3) (c) (12, 6) (d) (6, 1)
  27. 27.In which quadrant does the point (6, −7) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  28. 28.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 21 (c) 400 (d) 28
  29. 29.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 31 (c) 26 (d) 25
  30. 30.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 13 (c) 169 (d) 14
  31. 31.In which quadrant does the point (−4, −5) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  32. 32.In which quadrant does the point (−1, 1) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  33. 33.What is the midpoint of the line joining (7, 18) and (9, 8)? (a) (1, 5) (b) (16, 26) (c) (8, 13) (d) (13, 8)
  34. 34.What is the distance between the points (9, 8) and (12, 12)? (a) 7 (b) 5 (c) 25 (d) 6
  35. 35.In which quadrant does the point (2, 9) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  36. 36.In which quadrant does the point (−9, 7) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  37. 37.What is the midpoint of the line joining (3, 6) and (7, 12)? (a) (5, 9) (b) (10, 18) (c) (9, 5) (d) (2, 3)
  38. 38.In which quadrant does the point (−6, −8) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  39. 39.What is the distance between the points (1, 7) and (13, 2)? (a) 14 (b) 13 (c) 169 (d) 17
  40. 40.What is the distance between the points (2, 3) and (6, 6)? (a) 6 (b) 5 (c) 7 (d) 25

Answer key

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

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