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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 680 · 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, 9) and (4, 5)? (a) 25 (b) 5 (c) 7 (d) 6
  2. 2.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 6 (c) 5 (d) 25
  3. 3.In which quadrant does the point (5, 2) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  4. 4.What is the midpoint of the line joining (8, 6) and (12, 8)? (a) (20, 14) (b) (2, 1) (c) (10, 7) (d) (7, 10)
  5. 5.What is the distance between the points (5, 8) and (11, 0)? (a) 100 (b) 11 (c) 10 (d) 14
  6. 6.What is the distance between the points (6, 16) and (15, 4)? (a) 16 (b) 21 (c) 225 (d) 15
  7. 7.In which quadrant does the point (9, 8) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  8. 8.What is the midpoint of the line joining (4, 11) and (10, 5)? (a) (8, 7) (b) (3, 3) (c) (14, 16) (d) (7, 8)
  9. 9.What is the midpoint of the line joining (7, 8) and (19, 6)? (a) (26, 14) (b) (6, 1) (c) (13, 7) (d) (7, 13)
  10. 10.What is the distance between the points (1, 11) and (7, 3)? (a) 14 (b) 100 (c) 10 (d) 11
  11. 11.In which quadrant does the point (2, 8) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  12. 12.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 16 (c) 15 (d) 225
  13. 13.What is the midpoint of the line joining (2, 4) and (12, 8)? (a) (5, 2) (b) (14, 12) (c) (6, 7) (d) (7, 6)
  14. 14.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 21 (c) 20 (d) 400
  15. 15.What is the midpoint of the line joining (9, 11) and (17, 1)? (a) (6, 13) (b) (4, 5) (c) (13, 6) (d) (26, 12)
  16. 16.In which quadrant does the point (−2, −3) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  17. 17.How far is the point (12, 5) from the origin (0, 0)? (a) 13 (b) 17 (c) 14 (d) 169
  18. 18.In which quadrant does the point (1, 7) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  19. 19.What is the distance between the points (7, 6) and (19, 11)? (a) 169 (b) 13 (c) 14 (d) 17
  20. 20.What is the distance between the points (9, 4) and (21, 9)? (a) 13 (b) 14 (c) 169 (d) 17
  21. 21.What is the distance between the points (2, 0) and (8, 8)? (a) 14 (b) 100 (c) 10 (d) 11
  22. 22.What is the distance between the points (0, 1) and (9, 13)? (a) 21 (b) 15 (c) 16 (d) 225
  23. 23.In which quadrant does the point (3, −7) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  24. 24.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 169 (c) 13 (d) 14
  25. 25.What is the midpoint of the line joining (0, 4) and (4, 0)? (a) (3, 2) (b) (4, 4) (c) (2, 3) (d) (2, 2)
  26. 26.What is the midpoint of the line joining (7, 9) and (17, 7)? (a) (8, 12) (b) (5, 1) (c) (12, 8) (d) (24, 16)
  27. 27.What is the distance between the points (3, 3) and (15, 19)? (a) 20 (b) 21 (c) 28 (d) 400
  28. 28.In which quadrant does the point (9, 4) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  29. 29.In which quadrant does the point (3, 8) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  30. 30.What is the distance between the points (0, 25) and (12, 9)? (a) 21 (b) 28 (c) 20 (d) 400
  31. 31.What is the midpoint of the line joining (3, 2) and (7, 0)? (a) (2, 1) (b) (1, 5) (c) (10, 2) (d) (5, 1)
  32. 32.What is the midpoint of the line joining (6, 20) and (10, 10)? (a) (16, 30) (b) (2, 5) (c) (15, 8) (d) (8, 15)
  33. 33.What is the distance between the points (2, 12) and (14, 3)? (a) 225 (b) 16 (c) 21 (d) 15
  34. 34.In which quadrant does the point (1, −7) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  35. 35.What is the distance between the points (6, 11) and (21, 3)? (a) 23 (b) 289 (c) 17 (d) 18
  36. 36.What is the midpoint of the line joining (8, 1) and (16, 11)? (a) (12, 6) (b) (24, 12) (c) (4, 5) (d) (6, 12)
  37. 37.What is the distance between the points (8, 0) and (13, 12)? (a) 13 (b) 17 (c) 14 (d) 169
  38. 38.What is the distance between the points (8, 7) and (16, 22)? (a) 23 (b) 18 (c) 289 (d) 17
  39. 39.In which quadrant does the point (6, 7) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  40. 40.What is the midpoint of the line joining (8, 14) and (18, 10)? (a) (13, 12) (b) (5, 2) (c) (26, 24) (d) (12, 13)

Answer key

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

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