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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 404 · 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 (4, 3) from the origin (0, 0)? (a) 5 (b) 6 (c) 25 (d) 7
  2. 2.In which quadrant does the point (5, 4) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  3. 3.What is the distance between the points (1, 8) and (16, 16)? (a) 289 (b) 23 (c) 17 (d) 18
  4. 4.What is the midpoint of the line joining (6, 8) and (16, 18)? (a) (13, 11) (b) (11, 13) (c) (22, 26) (d) (5, 5)
  5. 5.What is the distance between the points (6, 9) and (14, 15)? (a) 100 (b) 10 (c) 11 (d) 14
  6. 6.What is the distance between the points (2, 3) and (8, 11)? (a) 11 (b) 100 (c) 10 (d) 14
  7. 7.What is the midpoint of the line joining (6, 1) and (14, 9)? (a) (5, 10) (b) (20, 10) (c) (10, 5) (d) (4, 4)
  8. 8.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 26 (c) 25 (d) 31
  9. 9.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 100 (c) 11 (d) 14
  10. 10.What is the midpoint of the line joining (7, 9) and (19, 7)? (a) (13, 8) (b) (8, 13) (c) (26, 16) (d) (6, 1)
  11. 11.In which quadrant does the point (−9, 2) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  12. 12.In which quadrant does the point (−1, −6) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  13. 13.What is the distance between the points (2, 28) and (9, 4)? (a) 25 (b) 26 (c) 31 (d) 625
  14. 14.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 169 (c) 14 (d) 13
  15. 15.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 17 (c) 18 (d) 23
  16. 16.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 18 (c) 289 (d) 17
  17. 17.What is the distance between the points (6, 6) and (18, 1)? (a) 169 (b) 13 (c) 17 (d) 14
  18. 18.What is the midpoint of the line joining (4, 12) and (10, 4)? (a) (14, 16) (b) (8, 7) (c) (7, 8) (d) (3, 4)
  19. 19.What is the distance between the points (6, 9) and (15, 21)? (a) 16 (b) 225 (c) 15 (d) 21
  20. 20.What is the midpoint of the line joining (10, 10) and (12, 8)? (a) (1, 1) (b) (22, 18) (c) (9, 11) (d) (11, 9)
  21. 21.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 21 (c) 400 (d) 20
  22. 22.What is the distance between the points (3, 18) and (12, 6)? (a) 225 (b) 15 (c) 16 (d) 21
  23. 23.What is the distance between the points (5, 1) and (20, 9)? (a) 17 (b) 23 (c) 18 (d) 289
  24. 24.In which quadrant does the point (4, −3) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  25. 25.In which quadrant does the point (6, 6) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  26. 26.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 20 (c) 400 (d) 21
  27. 27.What is the midpoint of the line joining (3, 3) and (11, 13)? (a) (14, 16) (b) (8, 7) (c) (7, 8) (d) (4, 5)
  28. 28.What is the distance between the points (1, 22) and (13, 6)? (a) 21 (b) 400 (c) 20 (d) 28
  29. 29.What is the midpoint of the line joining (0, 4) and (6, 14)? (a) (6, 18) (b) (3, 5) (c) (9, 3) (d) (3, 9)
  30. 30.What is the midpoint of the line joining (3, 4) and (7, 8)? (a) (10, 12) (b) (2, 2) (c) (5, 6) (d) (6, 5)
  31. 31.In which quadrant does the point (9, −4) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  32. 32.In which quadrant does the point (5, −6) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  33. 33.What is the distance between the points (2, 19) and (7, 7)? (a) 13 (b) 14 (c) 17 (d) 169
  34. 34.What is the distance between the points (3, 8) and (19, 20)? (a) 21 (b) 28 (c) 400 (d) 20
  35. 35.What is the midpoint of the line joining (0, 2) and (6, 12)? (a) (3, 7) (b) (6, 14) (c) (7, 3) (d) (3, 5)
  36. 36.What is the midpoint of the line joining (6, 0) and (18, 10)? (a) (24, 10) (b) (12, 5) (c) (5, 12) (d) (6, 5)
  37. 37.In which quadrant does the point (−5, 2) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  38. 38.What is the distance between the points (4, 2) and (12, 8)? (a) 11 (b) 100 (c) 14 (d) 10
  39. 39.What is the midpoint of the line joining (10, 9) and (18, 3)? (a) (4, 3) (b) (14, 6) (c) (28, 12) (d) (6, 14)
  40. 40.What is the midpoint of the line joining (9, 3) and (15, 15)? (a) (12, 9) (b) (3, 6) (c) (9, 12) (d) (24, 18)

Answer key

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

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