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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 342 · 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 (9, 9) and (15, 1)? (a) 100 (b) 14 (c) 10 (d) 11
  2. 2.In which quadrant does the point (−4, −8) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  3. 3.What is the distance between the points (6, 1) and (13, 25)? (a) 25 (b) 31 (c) 625 (d) 26
  4. 4.In which quadrant does the point (−7, 4) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  5. 5.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 6 (c) 7 (d) 5
  6. 6.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 21 (c) 28 (d) 20
  7. 7.What is the midpoint of the line joining (0, 6) and (10, 16)? (a) (5, 11) (b) (5, 5) (c) (10, 22) (d) (11, 5)
  8. 8.What is the midpoint of the line joining (7, 12) and (11, 8)? (a) (2, 2) (b) (9, 10) (c) (10, 9) (d) (18, 20)
  9. 9.In which quadrant does the point (6, −8) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  10. 10.What is the distance between the points (7, 0) and (15, 6)? (a) 10 (b) 14 (c) 11 (d) 100
  11. 11.In which quadrant does the point (−6, 3) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  12. 12.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 14 (c) 13 (d) 17
  13. 13.What is the midpoint of the line joining (8, 6) and (14, 12)? (a) (9, 11) (b) (22, 18) (c) (3, 3) (d) (11, 9)
  14. 14.What is the midpoint of the line joining (3, 3) and (7, 1)? (a) (10, 4) (b) (5, 2) (c) (2, 1) (d) (2, 5)
  15. 15.In which quadrant does the point (1, 1) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  16. 16.What is the distance between the points (9, 8) and (33, 1)? (a) 31 (b) 625 (c) 26 (d) 25
  17. 17.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 31 (c) 25 (d) 26
  18. 18.What is the distance between the points (9, 16) and (21, 7)? (a) 225 (b) 16 (c) 15 (d) 21
  19. 19.What is the distance between the points (1, 6) and (5, 9)? (a) 6 (b) 5 (c) 7 (d) 25
  20. 20.What is the distance between the points (8, 4) and (12, 1)? (a) 25 (b) 5 (c) 6 (d) 7
  21. 21.What is the distance between the points (0, 8) and (4, 5)? (a) 7 (b) 25 (c) 5 (d) 6
  22. 22.What is the distance between the points (9, 14) and (25, 2)? (a) 21 (b) 20 (c) 28 (d) 400
  23. 23.What is the distance between the points (5, 18) and (10, 6)? (a) 13 (b) 17 (c) 169 (d) 14
  24. 24.In which quadrant does the point (5, 2) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  25. 25.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 6 (c) 5 (d) 25
  26. 26.What is the midpoint of the line joining (3, 14) and (11, 2)? (a) (7, 8) (b) (8, 7) (c) (4, 6) (d) (14, 16)
  27. 27.In which quadrant does the point (−6, 1) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  28. 28.What is the midpoint of the line joining (3, 7) and (7, 11)? (a) (10, 18) (b) (5, 9) (c) (2, 2) (d) (9, 5)
  29. 29.In which quadrant does the point (5, −4) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  30. 30.In which quadrant does the point (2, −9) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  31. 31.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 10 (c) 100 (d) 11
  32. 32.What is the distance between the points (4, 13) and (19, 5)? (a) 23 (b) 289 (c) 17 (d) 18
  33. 33.How far is the point (9, 12) from the origin (0, 0)? (a) 15 (b) 16 (c) 21 (d) 225
  34. 34.In which quadrant does the point (−7, 8) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  35. 35.How far is the point (7, 24) from the origin (0, 0)? (a) 25 (b) 31 (c) 26 (d) 625
  36. 36.What is the midpoint of the line joining (1, 9) and (5, 21)? (a) (6, 30) (b) (2, 6) (c) (3, 15) (d) (15, 3)
  37. 37.What is the midpoint of the line joining (6, 2) and (8, 4)? (a) (14, 6) (b) (7, 3) (c) (3, 7) (d) (1, 1)
  38. 38.What is the midpoint of the line joining (0, 9) and (2, 5)? (a) (1, 2) (b) (1, 7) (c) (7, 1) (d) (2, 14)
  39. 39.In which quadrant does the point (7, −9) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  40. 40.What is the midpoint of the line joining (10, 10) and (22, 18)? (a) (6, 4) (b) (32, 28) (c) (14, 16) (d) (16, 14)

Answer key

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

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