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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 304 · 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 midpoint of the line joining (6, 2) and (16, 8)? (a) (5, 11) (b) (11, 5) (c) (22, 10) (d) (5, 3)
  2. 2.What is the distance between the points (9, 9) and (24, 1)? (a) 18 (b) 17 (c) 23 (d) 289
  3. 3.What is the midpoint of the line joining (6, 5) and (16, 1)? (a) (5, 2) (b) (22, 6) (c) (11, 3) (d) (3, 11)
  4. 4.What is the distance between the points (3, 1) and (11, 16)? (a) 17 (b) 23 (c) 18 (d) 289
  5. 5.In which quadrant does the point (−9, −1) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  6. 6.What is the midpoint of the line joining (4, 6) and (12, 14)? (a) (10, 8) (b) (16, 20) (c) (4, 4) (d) (8, 10)
  7. 7.How far is the point (12, 16) from the origin (0, 0)? (a) 20 (b) 21 (c) 400 (d) 28
  8. 8.What is the distance between the points (6, 0) and (12, 8)? (a) 14 (b) 11 (c) 10 (d) 100
  9. 9.What is the distance between the points (1, 19) and (6, 7)? (a) 14 (b) 13 (c) 169 (d) 17
  10. 10.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 225 (c) 16 (d) 15
  11. 11.In which quadrant does the point (4, −5) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  12. 12.In which quadrant does the point (−2, −5) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  13. 13.How far is the point (4, 3) from the origin (0, 0)? (a) 5 (b) 7 (c) 6 (d) 25
  14. 14.In which quadrant does the point (4, 9) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  15. 15.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 21 (c) 400 (d) 20
  16. 16.What is the midpoint of the line joining (9, 9) and (13, 17)? (a) (22, 26) (b) (13, 11) (c) (11, 13) (d) (2, 4)
  17. 17.In which quadrant does the point (4, 1) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  18. 18.In which quadrant does the point (−2, −1) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  19. 19.In which quadrant does the point (2, 3) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  20. 20.In which quadrant does the point (6, 5) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  21. 21.In which quadrant does the point (6, −4) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  22. 22.What is the midpoint of the line joining (8, 5) and (16, 15)? (a) (4, 5) (b) (10, 12) (c) (24, 20) (d) (12, 10)
  23. 23.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 26 (c) 25 (d) 625
  24. 24.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 100 (c) 11 (d) 10
  25. 25.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 17 (c) 169 (d) 13
  26. 26.In which quadrant does the point (−5, 7) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  27. 27.What is the distance between the points (0, 16) and (15, 8)? (a) 23 (b) 289 (c) 18 (d) 17
  28. 28.What is the midpoint of the line joining (10, 1) and (14, 5)? (a) (12, 3) (b) (3, 12) (c) (2, 2) (d) (24, 6)
  29. 29.What is the distance between the points (2, 1) and (14, 10)? (a) 16 (b) 21 (c) 15 (d) 225
  30. 30.What is the distance between the points (5, 16) and (13, 1)? (a) 289 (b) 23 (c) 17 (d) 18
  31. 31.What is the distance between the points (5, 2) and (20, 10)? (a) 289 (b) 17 (c) 18 (d) 23
  32. 32.What is the distance between the points (9, 6) and (17, 0)? (a) 100 (b) 10 (c) 14 (d) 11
  33. 33.What is the distance between the points (9, 18) and (21, 9)? (a) 15 (b) 225 (c) 16 (d) 21
  34. 34.What is the distance between the points (9, 13) and (33, 6)? (a) 625 (b) 26 (c) 31 (d) 25
  35. 35.What is the distance between the points (3, 0) and (18, 8)? (a) 17 (b) 23 (c) 289 (d) 18
  36. 36.How far is the point (7, 24) from the origin (0, 0)? (a) 25 (b) 31 (c) 625 (d) 26
  37. 37.What is the midpoint of the line joining (8, 2) and (14, 10)? (a) (3, 4) (b) (11, 6) (c) (6, 11) (d) (22, 12)
  38. 38.What is the midpoint of the line joining (2, 7) and (10, 3)? (a) (5, 6) (b) (12, 10) (c) (4, 2) (d) (6, 5)
  39. 39.In which quadrant does the point (−7, −4) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  40. 40.What is the distance between the points (4, 0) and (16, 9)? (a) 21 (b) 15 (c) 225 (d) 16

Answer key

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

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