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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 371 · 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, 15) from the origin (0, 0)? (a) 23 (b) 289 (c) 18 (d) 17
  2. 2.In which quadrant does the point (−9, −8) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  3. 3.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 10 (c) 100 (d) 14
  4. 4.What is the midpoint of the line joining (8, 10) and (14, 0)? (a) (3, 5) (b) (22, 10) (c) (5, 11) (d) (11, 5)
  5. 5.What is the midpoint of the line joining (3, 1) and (13, 5)? (a) (8, 3) (b) (3, 8) (c) (5, 2) (d) (16, 6)
  6. 6.What is the distance between the points (2, 7) and (14, 12)? (a) 169 (b) 14 (c) 17 (d) 13
  7. 7.What is the distance between the points (0, 4) and (16, 16)? (a) 28 (b) 21 (c) 20 (d) 400
  8. 8.What is the distance between the points (3, 7) and (15, 23)? (a) 21 (b) 400 (c) 20 (d) 28
  9. 9.In which quadrant does the point (6, −1) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  10. 10.In which quadrant does the point (8, 6) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  11. 11.What is the midpoint of the line joining (9, 4) and (19, 10)? (a) (7, 14) (b) (28, 14) (c) (5, 3) (d) (14, 7)
  12. 12.What is the midpoint of the line joining (5, 6) and (9, 0)? (a) (14, 6) (b) (2, 3) (c) (3, 7) (d) (7, 3)
  13. 13.What is the midpoint of the line joining (2, 0) and (14, 12)? (a) (6, 8) (b) (16, 12) (c) (8, 6) (d) (6, 6)
  14. 14.What is the distance between the points (0, 0) and (7, 24)? (a) 31 (b) 25 (c) 625 (d) 26
  15. 15.What is the distance between the points (1, 0) and (5, 3)? (a) 6 (b) 7 (c) 5 (d) 25
  16. 16.In which quadrant does the point (−7, 9) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  17. 17.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 6 (c) 7 (d) 25
  18. 18.In which quadrant does the point (−4, −7) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  19. 19.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 28 (c) 400 (d) 20
  20. 20.In which quadrant does the point (2, 9) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  21. 21.What is the midpoint of the line joining (10, 15) and (22, 7)? (a) (32, 22) (b) (16, 11) (c) (6, 4) (d) (11, 16)
  22. 22.What is the midpoint of the line joining (3, 6) and (7, 12)? (a) (5, 9) (b) (10, 18) (c) (9, 5) (d) (2, 3)
  23. 23.What is the distance between the points (9, 2) and (21, 7)? (a) 169 (b) 14 (c) 13 (d) 17
  24. 24.What is the midpoint of the line joining (6, 9) and (8, 3)? (a) (7, 6) (b) (1, 3) (c) (14, 12) (d) (6, 7)
  25. 25.What is the distance between the points (4, 4) and (8, 7)? (a) 6 (b) 25 (c) 5 (d) 7
  26. 26.In which quadrant does the point (−9, −4) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  27. 27.What is the midpoint of the line joining (4, 5) and (16, 17)? (a) (20, 22) (b) (10, 11) (c) (11, 10) (d) (6, 6)
  28. 28.What is the distance between the points (0, 8) and (6, 16)? (a) 11 (b) 100 (c) 14 (d) 10
  29. 29.What is the midpoint of the line joining (9, 7) and (13, 1)? (a) (2, 3) (b) (22, 8) (c) (11, 4) (d) (4, 11)
  30. 30.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 16 (c) 225 (d) 15
  31. 31.What is the midpoint of the line joining (0, 1) and (6, 13)? (a) (3, 7) (b) (7, 3) (c) (6, 14) (d) (3, 6)
  32. 32.What is the distance between the points (7, 10) and (13, 2)? (a) 10 (b) 100 (c) 14 (d) 11
  33. 33.What is the midpoint of the line joining (4, 13) and (8, 9)? (a) (2, 2) (b) (6, 11) (c) (11, 6) (d) (12, 22)
  34. 34.What is the distance between the points (6, 7) and (18, 23)? (a) 20 (b) 21 (c) 28 (d) 400
  35. 35.In which quadrant does the point (8, 9) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  36. 36.In which quadrant does the point (−4, 7) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  37. 37.In which quadrant does the point (2, 5) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  38. 38.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 25 (c) 26 (d) 31
  39. 39.What is the distance between the points (8, 9) and (14, 1)? (a) 10 (b) 11 (c) 14 (d) 100
  40. 40.What is the distance between the points (8, 10) and (16, 4)? (a) 100 (b) 11 (c) 10 (d) 14

Answer key

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

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