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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 686 · 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 (8, 6) from the origin (0, 0)? (a) 10 (b) 11 (c) 14 (d) 100
  2. 2.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 15 (c) 21 (d) 225
  3. 3.What is the distance between the points (6, 13) and (30, 6)? (a) 26 (b) 31 (c) 625 (d) 25
  4. 4.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 17 (c) 23 (d) 289
  5. 5.In which quadrant does the point (3, 7) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  6. 6.What is the distance between the points (4, 16) and (28, 9)? (a) 625 (b) 26 (c) 31 (d) 25
  7. 7.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 5 (c) 25 (d) 6
  8. 8.What is the midpoint of the line joining (3, 2) and (13, 8)? (a) (5, 8) (b) (5, 3) (c) (16, 10) (d) (8, 5)
  9. 9.In which quadrant does the point (−1, 6) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  10. 10.What is the midpoint of the line joining (2, 0) and (6, 2)? (a) (4, 1) (b) (2, 1) (c) (8, 2) (d) (1, 4)
  11. 11.What is the distance between the points (7, 3) and (14, 27)? (a) 25 (b) 26 (c) 625 (d) 31
  12. 12.What is the midpoint of the line joining (7, 9) and (9, 11)? (a) (1, 1) (b) (16, 20) (c) (10, 8) (d) (8, 10)
  13. 13.What is the midpoint of the line joining (2, 5) and (10, 3)? (a) (4, 1) (b) (4, 6) (c) (6, 4) (d) (12, 8)
  14. 14.What is the midpoint of the line joining (0, 3) and (10, 5)? (a) (4, 5) (b) (5, 1) (c) (10, 8) (d) (5, 4)
  15. 15.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 6 (c) 5 (d) 7
  16. 16.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 25 (c) 26 (d) 625
  17. 17.In which quadrant does the point (−9, −9) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  18. 18.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 11 (c) 14 (d) 10
  19. 19.What is the distance between the points (2, 18) and (10, 3)? (a) 23 (b) 17 (c) 289 (d) 18
  20. 20.What is the midpoint of the line joining (7, 4) and (19, 8)? (a) (13, 6) (b) (6, 2) (c) (26, 12) (d) (6, 13)
  21. 21.What is the distance between the points (0, 13) and (5, 1)? (a) 17 (b) 169 (c) 13 (d) 14
  22. 22.In which quadrant does the point (3, −9) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  23. 23.What is the midpoint of the line joining (7, 7) and (9, 15)? (a) (11, 8) (b) (16, 22) (c) (1, 4) (d) (8, 11)
  24. 24.How far is the point (12, 9) from the origin (0, 0)? (a) 15 (b) 225 (c) 21 (d) 16
  25. 25.What is the midpoint of the line joining (3, 5) and (11, 7)? (a) (6, 7) (b) (4, 1) (c) (7, 6) (d) (14, 12)
  26. 26.What is the midpoint of the line joining (8, 4) and (20, 2)? (a) (3, 14) (b) (28, 6) (c) (6, 1) (d) (14, 3)
  27. 27.What is the distance between the points (6, 13) and (18, 8)? (a) 169 (b) 14 (c) 13 (d) 17
  28. 28.What is the distance between the points (8, 5) and (15, 29)? (a) 31 (b) 26 (c) 625 (d) 25
  29. 29.What is the distance between the points (8, 6) and (17, 18)? (a) 21 (b) 16 (c) 225 (d) 15
  30. 30.What is the midpoint of the line joining (7, 5) and (19, 1)? (a) (26, 6) (b) (13, 3) (c) (3, 13) (d) (6, 2)
  31. 31.In which quadrant does the point (−3, −7) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  32. 32.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 13 (c) 14 (d) 169
  33. 33.In which quadrant does the point (1, 1) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  34. 34.What is the midpoint of the line joining (2, 12) and (4, 0)? (a) (6, 3) (b) (1, 6) (c) (3, 6) (d) (6, 12)
  35. 35.In which quadrant does the point (−2, −9) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  36. 36.What is the distance between the points (3, 2) and (9, 10)? (a) 11 (b) 14 (c) 100 (d) 10
  37. 37.What is the distance between the points (1, 26) and (8, 2)? (a) 625 (b) 25 (c) 31 (d) 26
  38. 38.What is the distance between the points (0, 9) and (5, 21)? (a) 17 (b) 14 (c) 13 (d) 169
  39. 39.What is the midpoint of the line joining (6, 16) and (12, 8)? (a) (18, 24) (b) (9, 12) (c) (3, 4) (d) (12, 9)
  40. 40.What is the midpoint of the line joining (4, 3) and (10, 1)? (a) (2, 7) (b) (3, 1) (c) (14, 4) (d) (7, 2)

Answer key

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

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