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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 523 · 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 (3, 29) and (10, 5)? (a) 26 (b) 25 (c) 31 (d) 625
  2. 2.In which quadrant does the point (−6, −5) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  3. 3.In which quadrant does the point (−3, 8) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  4. 4.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 11 (c) 14 (d) 100
  5. 5.What is the distance between the points (4, 20) and (13, 8)? (a) 21 (b) 225 (c) 16 (d) 15
  6. 6.What is the distance between the points (8, 3) and (15, 27)? (a) 25 (b) 625 (c) 26 (d) 31
  7. 7.What is the midpoint of the line joining (8, 1) and (10, 7)? (a) (4, 9) (b) (9, 4) (c) (1, 3) (d) (18, 8)
  8. 8.In which quadrant does the point (4, 6) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  9. 9.What is the midpoint of the line joining (1, 20) and (7, 10)? (a) (8, 30) (b) (15, 4) (c) (3, 5) (d) (4, 15)
  10. 10.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 25 (c) 7 (d) 5
  11. 11.What is the midpoint of the line joining (1, 5) and (11, 1)? (a) (6, 3) (b) (3, 6) (c) (12, 6) (d) (5, 2)
  12. 12.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 21 (c) 20 (d) 400
  13. 13.In which quadrant does the point (−7, 1) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  14. 14.What is the midpoint of the line joining (10, 1) and (12, 3)? (a) (1, 1) (b) (2, 11) (c) (11, 2) (d) (22, 4)
  15. 15.What is the midpoint of the line joining (2, 9) and (14, 1)? (a) (6, 4) (b) (8, 5) (c) (16, 10) (d) (5, 8)
  16. 16.In which quadrant does the point (5, 2) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  17. 17.In which quadrant does the point (−9, 1) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  18. 18.What is the midpoint of the line joining (0, 19) and (6, 9)? (a) (3, 5) (b) (6, 28) (c) (3, 14) (d) (14, 3)
  19. 19.What is the midpoint of the line joining (3, 11) and (13, 3)? (a) (8, 7) (b) (5, 4) (c) (7, 8) (d) (16, 14)
  20. 20.What is the midpoint of the line joining (5, 14) and (7, 6)? (a) (10, 6) (b) (12, 20) (c) (1, 4) (d) (6, 10)
  21. 21.What is the distance between the points (0, 26) and (7, 2)? (a) 31 (b) 26 (c) 25 (d) 625
  22. 22.What is the midpoint of the line joining (2, 7) and (6, 5)? (a) (2, 1) (b) (6, 4) (c) (4, 6) (d) (8, 12)
  23. 23.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 625 (c) 26 (d) 25
  24. 24.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 10 (c) 14 (d) 11
  25. 25.In which quadrant does the point (8, −3) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  26. 26.What is the distance between the points (2, 0) and (5, 4)? (a) 25 (b) 6 (c) 5 (d) 7
  27. 27.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 25 (c) 6 (d) 5
  28. 28.What is the midpoint of the line joining (6, 21) and (18, 9)? (a) (24, 30) (b) (12, 15) (c) (15, 12) (d) (6, 6)
  29. 29.What is the distance between the points (3, 5) and (11, 20)? (a) 18 (b) 23 (c) 289 (d) 17
  30. 30.In which quadrant does the point (−8, 8) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  31. 31.In which quadrant does the point (−6, −8) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  32. 32.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 18 (c) 289 (d) 17
  33. 33.What is the midpoint of the line joining (6, 17) and (18, 9)? (a) (24, 26) (b) (13, 12) (c) (6, 4) (d) (12, 13)
  34. 34.What is the midpoint of the line joining (4, 13) and (16, 1)? (a) (10, 7) (b) (7, 10) (c) (20, 14) (d) (6, 6)
  35. 35.What is the midpoint of the line joining (6, 4) and (16, 2)? (a) (3, 11) (b) (22, 6) (c) (11, 3) (d) (5, 1)
  36. 36.What is the midpoint of the line joining (5, 10) and (7, 4)? (a) (6, 7) (b) (12, 14) (c) (1, 3) (d) (7, 6)
  37. 37.In which quadrant does the point (−5, −2) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  38. 38.What is the distance between the points (5, 8) and (20, 16)? (a) 289 (b) 17 (c) 18 (d) 23
  39. 39.In which quadrant does the point (−5, 9) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  40. 40.What is the midpoint of the line joining (1, 7) and (7, 17)? (a) (4, 12) (b) (8, 24) (c) (3, 5) (d) (12, 4)

Answer key

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

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