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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 410 · 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.In which quadrant does the point (−5, 3) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  2. 2.What is the distance between the points (8, 5) and (32, 12)? (a) 625 (b) 26 (c) 31 (d) 25
  3. 3.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 14 (c) 17 (d) 13
  4. 4.What is the distance between the points (0, 6) and (7, 30)? (a) 625 (b) 31 (c) 25 (d) 26
  5. 5.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 25 (c) 31 (d) 26
  6. 6.What is the distance between the points (9, 5) and (33, 12)? (a) 26 (b) 31 (c) 625 (d) 25
  7. 7.In which quadrant does the point (9, 3) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  8. 8.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 21 (c) 400 (d) 20
  9. 9.What is the midpoint of the line joining (3, 0) and (7, 10)? (a) (6, 5) (b) (2, 5) (c) (10, 10) (d) (5, 5)
  10. 10.In which quadrant does the point (−7, −4) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  11. 11.What is the distance between the points (2, 21) and (14, 5)? (a) 400 (b) 20 (c) 28 (d) 21
  12. 12.In which quadrant does the point (−7, 9) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  13. 13.What is the midpoint of the line joining (8, 10) and (10, 8)? (a) (18, 18) (b) (1, 1) (c) (10, 9) (d) (9, 9)
  14. 14.In which quadrant does the point (−3, 7) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  15. 15.What is the midpoint of the line joining (2, 2) and (4, 6)? (a) (1, 2) (b) (3, 4) (c) (6, 8) (d) (4, 3)
  16. 16.In which quadrant does the point (3, 4) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  17. 17.What is the distance between the points (6, 21) and (22, 9)? (a) 28 (b) 400 (c) 21 (d) 20
  18. 18.What is the midpoint of the line joining (3, 0) and (11, 12)? (a) (7, 6) (b) (6, 7) (c) (14, 12) (d) (4, 6)
  19. 19.How far is the point (9, 12) from the origin (0, 0)? (a) 15 (b) 225 (c) 21 (d) 16
  20. 20.What is the distance between the points (9, 2) and (18, 14)? (a) 21 (b) 16 (c) 225 (d) 15
  21. 21.What is the distance between the points (8, 3) and (13, 15)? (a) 169 (b) 14 (c) 13 (d) 17
  22. 22.What is the distance between the points (1, 3) and (4, 7)? (a) 7 (b) 25 (c) 5 (d) 6
  23. 23.What is the midpoint of the line joining (3, 7) and (13, 11)? (a) (5, 2) (b) (16, 18) (c) (8, 9) (d) (9, 8)
  24. 24.In which quadrant does the point (2, −4) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  25. 25.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 169 (c) 14 (d) 13
  26. 26.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 5 (c) 6 (d) 7
  27. 27.What is the midpoint of the line joining (0, 0) and (10, 10)? (a) (6, 5) (b) (10, 10) (c) (5, 5) (d) (5, 6)
  28. 28.What is the distance between the points (7, 3) and (12, 15)? (a) 169 (b) 13 (c) 17 (d) 14
  29. 29.What is the distance between the points (6, 12) and (18, 3)? (a) 225 (b) 21 (c) 15 (d) 16
  30. 30.What is the midpoint of the line joining (6, 5) and (16, 11)? (a) (22, 16) (b) (11, 8) (c) (5, 3) (d) (8, 11)
  31. 31.What is the distance between the points (0, 7) and (6, 15)? (a) 100 (b) 14 (c) 10 (d) 11
  32. 32.What is the midpoint of the line joining (2, 3) and (4, 9)? (a) (6, 12) (b) (1, 3) (c) (6, 3) (d) (3, 6)
  33. 33.What is the distance between the points (4, 7) and (12, 1)? (a) 10 (b) 14 (c) 11 (d) 100
  34. 34.What is the distance between the points (0, 5) and (6, 13)? (a) 14 (b) 10 (c) 11 (d) 100
  35. 35.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 10 (c) 100 (d) 11
  36. 36.In which quadrant does the point (−5, −6) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  37. 37.In which quadrant does the point (−9, 1) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  38. 38.What is the midpoint of the line joining (0, 9) and (12, 3)? (a) (12, 12) (b) (6, 3) (c) (7, 6) (d) (6, 6)
  39. 39.In which quadrant does the point (1, 2) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  40. 40.What is the distance between the points (1, 15) and (9, 9)? (a) 11 (b) 100 (c) 10 (d) 14

Answer key

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

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