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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 675 · 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 (7, 3) and (12, 15)? (a) 169 (b) 17 (c) 14 (d) 13
  2. 2.What is the distance between the points (6, 8) and (9, 12)? (a) 7 (b) 6 (c) 25 (d) 5
  3. 3.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 15 (c) 16 (d) 21
  4. 4.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 225 (c) 15 (d) 21
  5. 5.What is the distance between the points (2, 1) and (7, 13)? (a) 17 (b) 169 (c) 14 (d) 13
  6. 6.What is the midpoint of the line joining (1, 7) and (13, 5)? (a) (14, 12) (b) (7, 6) (c) (6, 7) (d) (6, 1)
  7. 7.In which quadrant does the point (−1, 6) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  8. 8.In which quadrant does the point (2, 7) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  9. 9.What is the midpoint of the line joining (7, 8) and (13, 16)? (a) (10, 12) (b) (3, 4) (c) (12, 10) (d) (20, 24)
  10. 10.What is the distance between the points (7, 1) and (10, 5)? (a) 25 (b) 6 (c) 5 (d) 7
  11. 11.What is the distance between the points (7, 16) and (23, 4)? (a) 400 (b) 21 (c) 20 (d) 28
  12. 12.In which quadrant does the point (4, −9) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  13. 13.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 289 (c) 23 (d) 17
  14. 14.What is the distance between the points (8, 4) and (11, 8)? (a) 5 (b) 6 (c) 25 (d) 7
  15. 15.What is the distance between the points (3, 4) and (6, 8)? (a) 6 (b) 25 (c) 7 (d) 5
  16. 16.What is the distance between the points (5, 5) and (9, 8)? (a) 5 (b) 25 (c) 6 (d) 7
  17. 17.What is the midpoint of the line joining (1, 1) and (5, 7)? (a) (4, 3) (b) (6, 8) (c) (3, 4) (d) (2, 3)
  18. 18.In which quadrant does the point (8, −4) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  19. 19.In which quadrant does the point (3, −7) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  20. 20.What is the distance between the points (4, 3) and (16, 12)? (a) 225 (b) 21 (c) 15 (d) 16
  21. 21.What is the distance between the points (8, 23) and (16, 8)? (a) 17 (b) 289 (c) 23 (d) 18
  22. 22.In which quadrant does the point (2, −5) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  23. 23.What is the distance between the points (2, 6) and (14, 1)? (a) 13 (b) 17 (c) 14 (d) 169
  24. 24.What is the distance between the points (2, 16) and (10, 1)? (a) 18 (b) 289 (c) 17 (d) 23
  25. 25.What is the distance between the points (6, 32) and (13, 8)? (a) 31 (b) 625 (c) 26 (d) 25
  26. 26.What is the midpoint of the line joining (10, 17) and (14, 5)? (a) (24, 22) (b) (11, 12) (c) (2, 6) (d) (12, 11)
  27. 27.In which quadrant does the point (−2, −2) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  28. 28.In which quadrant does the point (−8, −1) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  29. 29.What is the midpoint of the line joining (5, 4) and (15, 10)? (a) (5, 3) (b) (10, 7) (c) (7, 10) (d) (20, 14)
  30. 30.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 625 (c) 26 (d) 25
  31. 31.What is the midpoint of the line joining (3, 4) and (15, 14)? (a) (6, 5) (b) (9, 9) (c) (18, 18) (d) (10, 9)
  32. 32.What is the midpoint of the line joining (10, 8) and (18, 12)? (a) (14, 10) (b) (4, 2) (c) (10, 14) (d) (28, 20)
  33. 33.What is the midpoint of the line joining (5, 20) and (7, 10)? (a) (15, 6) (b) (1, 5) (c) (6, 15) (d) (12, 30)
  34. 34.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 14 (c) 13 (d) 17
  35. 35.What is the distance between the points (3, 1) and (27, 8)? (a) 26 (b) 625 (c) 25 (d) 31
  36. 36.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 100 (c) 10 (d) 11
  37. 37.In which quadrant does the point (−5, −2) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  38. 38.What is the distance between the points (0, 2) and (16, 14)? (a) 28 (b) 21 (c) 400 (d) 20
  39. 39.In which quadrant does the point (9, −1) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  40. 40.What is the distance between the points (8, 12) and (14, 4)? (a) 11 (b) 10 (c) 100 (d) 14

Answer key

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

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