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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 339 · 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 (15, 8) from the origin (0, 0)? (a) 23 (b) 17 (c) 18 (d) 289
  2. 2.What is the distance between the points (3, 4) and (12, 16)? (a) 21 (b) 16 (c) 15 (d) 225
  3. 3.What is the distance between the points (4, 2) and (20, 14)? (a) 400 (b) 21 (c) 20 (d) 28
  4. 4.What is the distance between the points (5, 9) and (10, 21)? (a) 14 (b) 169 (c) 13 (d) 17
  5. 5.In which quadrant does the point (2, 6) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  6. 6.What is the distance between the points (7, 14) and (12, 2)? (a) 17 (b) 14 (c) 13 (d) 169
  7. 7.In which quadrant does the point (9, −7) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  8. 8.What is the distance between the points (1, 5) and (4, 9)? (a) 7 (b) 5 (c) 25 (d) 6
  9. 9.What is the midpoint of the line joining (5, 10) and (11, 20)? (a) (8, 15) (b) (16, 30) (c) (15, 8) (d) (3, 5)
  10. 10.What is the distance between the points (5, 12) and (13, 6)? (a) 100 (b) 11 (c) 14 (d) 10
  11. 11.In which quadrant does the point (4, 3) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  12. 12.What is the midpoint of the line joining (4, 6) and (14, 2)? (a) (5, 2) (b) (4, 9) (c) (9, 4) (d) (18, 8)
  13. 13.What is the midpoint of the line joining (0, 8) and (4, 16)? (a) (4, 24) (b) (12, 2) (c) (2, 12) (d) (2, 4)
  14. 14.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 5 (c) 6 (d) 25
  15. 15.How far is the point (5, 12) from the origin (0, 0)? (a) 13 (b) 169 (c) 14 (d) 17
  16. 16.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 14 (c) 100 (d) 10
  17. 17.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 7 (c) 5 (d) 25
  18. 18.What is the distance between the points (1, 1) and (4, 5)? (a) 25 (b) 7 (c) 5 (d) 6
  19. 19.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 21 (c) 15 (d) 225
  20. 20.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 31 (c) 25 (d) 26
  21. 21.What is the midpoint of the line joining (6, 14) and (8, 4)? (a) (7, 9) (b) (14, 18) (c) (1, 5) (d) (9, 7)
  22. 22.In which quadrant does the point (−5, 9) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  23. 23.What is the midpoint of the line joining (6, 9) and (8, 21)? (a) (15, 7) (b) (14, 30) (c) (7, 15) (d) (1, 6)
  24. 24.What is the midpoint of the line joining (1, 13) and (9, 7)? (a) (10, 5) (b) (4, 3) (c) (5, 10) (d) (10, 20)
  25. 25.In which quadrant does the point (−8, −1) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  26. 26.How far is the point (12, 5) from the origin (0, 0)? (a) 13 (b) 17 (c) 169 (d) 14
  27. 27.What is the midpoint of the line joining (1, 14) and (9, 6)? (a) (4, 4) (b) (10, 20) (c) (10, 5) (d) (5, 10)
  28. 28.What is the distance between the points (7, 15) and (23, 3)? (a) 400 (b) 20 (c) 28 (d) 21
  29. 29.What is the midpoint of the line joining (5, 16) and (7, 8)? (a) (6, 12) (b) (1, 4) (c) (12, 6) (d) (12, 24)
  30. 30.What is the midpoint of the line joining (4, 9) and (14, 7)? (a) (9, 8) (b) (18, 16) (c) (8, 9) (d) (5, 1)
  31. 31.In which quadrant does the point (−6, 1) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  32. 32.What is the midpoint of the line joining (5, 10) and (15, 0)? (a) (5, 5) (b) (20, 10) (c) (10, 5) (d) (5, 10)
  33. 33.In which quadrant does the point (−6, 4) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  34. 34.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 15 (c) 16 (d) 21
  35. 35.What is the distance between the points (1, 11) and (4, 7)? (a) 25 (b) 5 (c) 7 (d) 6
  36. 36.In which quadrant does the point (−4, 3) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  37. 37.What is the distance between the points (0, 9) and (24, 2)? (a) 25 (b) 26 (c) 31 (d) 625
  38. 38.What is the midpoint of the line joining (1, 0) and (13, 12)? (a) (14, 12) (b) (7, 6) (c) (6, 7) (d) (6, 6)
  39. 39.In which quadrant does the point (−3, −7) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  40. 40.In which quadrant does the point (9, −9) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant

Answer key

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

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