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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 695 · 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 (7, 24) from the origin (0, 0)? (a) 625 (b) 31 (c) 25 (d) 26
  2. 2.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 25 (c) 31 (d) 26
  3. 3.What is the midpoint of the line joining (2, 18) and (14, 10)? (a) (8, 14) (b) (6, 4) (c) (16, 28) (d) (14, 8)
  4. 4.What is the midpoint of the line joining (1, 3) and (5, 5)? (a) (3, 4) (b) (2, 1) (c) (6, 8) (d) (4, 3)
  5. 5.What is the midpoint of the line joining (0, 1) and (6, 13)? (a) (6, 14) (b) (3, 6) (c) (3, 7) (d) (7, 3)
  6. 6.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 7 (c) 5 (d) 6
  7. 7.In which quadrant does the point (6, 9) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  8. 8.In which quadrant does the point (−8, 9) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  9. 9.What is the distance between the points (5, 11) and (17, 2)? (a) 15 (b) 16 (c) 21 (d) 225
  10. 10.What is the distance between the points (2, 1) and (10, 16)? (a) 18 (b) 23 (c) 289 (d) 17
  11. 11.What is the distance between the points (8, 6) and (13, 18)? (a) 169 (b) 13 (c) 17 (d) 14
  12. 12.In which quadrant does the point (−6, −6) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  13. 13.What is the distance between the points (9, 17) and (24, 9)? (a) 17 (b) 18 (c) 23 (d) 289
  14. 14.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 5 (c) 7 (d) 25
  15. 15.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 14 (c) 100 (d) 11
  16. 16.In which quadrant does the point (−9, 9) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  17. 17.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 20 (c) 21 (d) 400
  18. 18.What is the distance between the points (6, 19) and (14, 4)? (a) 23 (b) 18 (c) 289 (d) 17
  19. 19.What is the midpoint of the line joining (8, 16) and (14, 6)? (a) (22, 22) (b) (11, 11) (c) (12, 11) (d) (3, 5)
  20. 20.In which quadrant does the point (−7, −6) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  21. 21.What is the midpoint of the line joining (10, 5) and (18, 11)? (a) (8, 14) (b) (28, 16) (c) (14, 8) (d) (4, 3)
  22. 22.What is the distance between the points (6, 7) and (12, 15)? (a) 14 (b) 10 (c) 100 (d) 11
  23. 23.In which quadrant does the point (−9, 2) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  24. 24.In which quadrant does the point (−4, −7) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  25. 25.In which quadrant does the point (6, 3) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  26. 26.What is the midpoint of the line joining (2, 6) and (8, 12)? (a) (10, 18) (b) (3, 3) (c) (9, 5) (d) (5, 9)
  27. 27.What is the distance between the points (0, 2) and (24, 9)? (a) 25 (b) 625 (c) 31 (d) 26
  28. 28.What is the distance between the points (5, 13) and (14, 1)? (a) 15 (b) 21 (c) 16 (d) 225
  29. 29.What is the distance between the points (5, 5) and (21, 17)? (a) 21 (b) 28 (c) 20 (d) 400
  30. 30.What is the distance between the points (2, 1) and (14, 10)? (a) 21 (b) 16 (c) 15 (d) 225
  31. 31.In which quadrant does the point (2, 9) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  32. 32.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 100 (c) 11 (d) 10
  33. 33.What is the distance between the points (9, 30) and (16, 6)? (a) 625 (b) 31 (c) 26 (d) 25
  34. 34.In which quadrant does the point (8, −7) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  35. 35.In which quadrant does the point (2, −8) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  36. 36.What is the distance between the points (5, 9) and (8, 13)? (a) 5 (b) 25 (c) 7 (d) 6
  37. 37.In which quadrant does the point (−2, −6) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  38. 38.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 13 (c) 169 (d) 14
  39. 39.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 18 (c) 17 (d) 23
  40. 40.What is the distance between the points (3, 17) and (11, 2)? (a) 17 (b) 289 (c) 18 (d) 23

Answer key

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

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