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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 578 · 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 (8, 8) and (16, 2)? (a) (12, 5) (b) (5, 12) (c) (24, 10) (d) (4, 3)
  2. 2.What is the distance between the points (5, 3) and (9, 6)? (a) 5 (b) 25 (c) 6 (d) 7
  3. 3.What is the midpoint of the line joining (2, 6) and (12, 10)? (a) (8, 7) (b) (5, 2) (c) (14, 16) (d) (7, 8)
  4. 4.In which quadrant does the point (5, −9) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  5. 5.In which quadrant does the point (−6, 6) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  6. 6.What is the distance between the points (9, 6) and (17, 0)? (a) 14 (b) 11 (c) 10 (d) 100
  7. 7.What is the midpoint of the line joining (2, 17) and (14, 5)? (a) (16, 22) (b) (8, 11) (c) (6, 6) (d) (11, 8)
  8. 8.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 18 (c) 289 (d) 17
  9. 9.In which quadrant does the point (5, −3) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  10. 10.What is the distance between the points (1, 9) and (7, 17)? (a) 14 (b) 11 (c) 10 (d) 100
  11. 11.In which quadrant does the point (1, 6) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  12. 12.What is the distance between the points (8, 28) and (15, 4)? (a) 625 (b) 31 (c) 25 (d) 26
  13. 13.In which quadrant does the point (−7, 1) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  14. 14.What is the midpoint of the line joining (0, 10) and (2, 12)? (a) (2, 22) (b) (1, 11) (c) (1, 1) (d) (11, 1)
  15. 15.What is the midpoint of the line joining (10, 9) and (18, 13)? (a) (4, 2) (b) (28, 22) (c) (11, 14) (d) (14, 11)
  16. 16.What is the distance between the points (9, 5) and (33, 12)? (a) 26 (b) 25 (c) 625 (d) 31
  17. 17.What is the distance between the points (2, 13) and (18, 1)? (a) 400 (b) 20 (c) 21 (d) 28
  18. 18.How far is the point (9, 12) from the origin (0, 0)? (a) 15 (b) 225 (c) 21 (d) 16
  19. 19.What is the midpoint of the line joining (4, 7) and (12, 5)? (a) (16, 12) (b) (6, 8) (c) (4, 1) (d) (8, 6)
  20. 20.In which quadrant does the point (5, 6) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  21. 21.In which quadrant does the point (−9, 1) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  22. 22.What is the distance between the points (4, 13) and (20, 1)? (a) 20 (b) 400 (c) 28 (d) 21
  23. 23.What is the distance between the points (0, 3) and (4, 0)? (a) 7 (b) 6 (c) 25 (d) 5
  24. 24.How far is the point (5, 12) from the origin (0, 0)? (a) 13 (b) 14 (c) 17 (d) 169
  25. 25.What is the midpoint of the line joining (1, 9) and (3, 21)? (a) (2, 15) (b) (4, 30) (c) (15, 2) (d) (1, 6)
  26. 26.What is the distance between the points (3, 18) and (15, 2)? (a) 400 (b) 21 (c) 28 (d) 20
  27. 27.In which quadrant does the point (−3, −4) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  28. 28.In which quadrant does the point (7, 5) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  29. 29.What is the distance between the points (6, 14) and (30, 7)? (a) 625 (b) 25 (c) 26 (d) 31
  30. 30.In which quadrant does the point (5, −5) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  31. 31.What is the midpoint of the line joining (1, 2) and (7, 6)? (a) (5, 4) (b) (8, 8) (c) (4, 4) (d) (3, 2)
  32. 32.What is the distance between the points (1, 6) and (9, 12)? (a) 11 (b) 14 (c) 10 (d) 100
  33. 33.What is the distance between the points (3, 10) and (11, 4)? (a) 14 (b) 10 (c) 11 (d) 100
  34. 34.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 18 (c) 23 (d) 289
  35. 35.What is the distance between the points (6, 5) and (10, 8)? (a) 7 (b) 5 (c) 25 (d) 6
  36. 36.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 25 (c) 26 (d) 31
  37. 37.What is the distance between the points (0, 2) and (12, 11)? (a) 225 (b) 15 (c) 16 (d) 21
  38. 38.What is the distance between the points (4, 8) and (9, 20)? (a) 17 (b) 14 (c) 13 (d) 169
  39. 39.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 25 (c) 5 (d) 7
  40. 40.What is the midpoint of the line joining (9, 5) and (21, 7)? (a) (6, 15) (b) (6, 1) (c) (15, 6) (d) (30, 12)

Answer key

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

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