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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 488 · 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 (3, 4) from the origin (0, 0)? (a) 25 (b) 7 (c) 5 (d) 6
  2. 2.In which quadrant does the point (1, 5) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  3. 3.What is the distance between the points (1, 13) and (25, 6)? (a) 26 (b) 31 (c) 625 (d) 25
  4. 4.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 6 (c) 5 (d) 25
  5. 5.In which quadrant does the point (−4, −1) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  6. 6.What is the distance between the points (4, 5) and (12, 11)? (a) 11 (b) 100 (c) 10 (d) 14
  7. 7.In which quadrant does the point (−2, 1) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  8. 8.What is the midpoint of the line joining (1, 12) and (11, 8)? (a) (12, 20) (b) (5, 2) (c) (6, 10) (d) (10, 6)
  9. 9.What is the distance between the points (3, 18) and (19, 6)? (a) 20 (b) 21 (c) 28 (d) 400
  10. 10.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 625 (c) 26 (d) 25
  11. 11.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 169 (c) 13 (d) 17
  12. 12.What is the midpoint of the line joining (1, 0) and (5, 4)? (a) (3, 2) (b) (2, 2) (c) (6, 4) (d) (2, 3)
  13. 13.What is the distance between the points (8, 5) and (20, 21)? (a) 400 (b) 28 (c) 20 (d) 21
  14. 14.What is the midpoint of the line joining (4, 9) and (12, 5)? (a) (7, 8) (b) (16, 14) (c) (4, 2) (d) (8, 7)
  15. 15.What is the midpoint of the line joining (8, 1) and (12, 9)? (a) (2, 4) (b) (5, 10) (c) (10, 5) (d) (20, 10)
  16. 16.What is the distance between the points (0, 8) and (16, 20)? (a) 28 (b) 21 (c) 400 (d) 20
  17. 17.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 31 (c) 25 (d) 26
  18. 18.How far is the point (12, 9) from the origin (0, 0)? (a) 16 (b) 21 (c) 15 (d) 225
  19. 19.What is the distance between the points (6, 5) and (30, 12)? (a) 26 (b) 25 (c) 625 (d) 31
  20. 20.In which quadrant does the point (2, −1) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  21. 21.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 21 (c) 16 (d) 15
  22. 22.What is the distance between the points (1, 21) and (6, 9)? (a) 17 (b) 169 (c) 14 (d) 13
  23. 23.In which quadrant does the point (−6, 5) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  24. 24.What is the distance between the points (7, 0) and (10, 4)? (a) 25 (b) 7 (c) 5 (d) 6
  25. 25.What is the midpoint of the line joining (1, 16) and (5, 8)? (a) (6, 24) (b) (2, 4) (c) (3, 12) (d) (12, 3)
  26. 26.What is the distance between the points (0, 16) and (6, 8)? (a) 11 (b) 14 (c) 10 (d) 100
  27. 27.What is the midpoint of the line joining (2, 2) and (8, 10)? (a) (5, 6) (b) (3, 4) (c) (10, 12) (d) (6, 5)
  28. 28.What is the distance between the points (6, 3) and (15, 15)? (a) 16 (b) 15 (c) 225 (d) 21
  29. 29.What is the distance between the points (7, 3) and (14, 27)? (a) 25 (b) 26 (c) 31 (d) 625
  30. 30.What is the midpoint of the line joining (4, 8) and (10, 4)? (a) (3, 2) (b) (6, 7) (c) (7, 6) (d) (14, 12)
  31. 31.What is the distance between the points (2, 24) and (14, 8)? (a) 400 (b) 20 (c) 21 (d) 28
  32. 32.In which quadrant does the point (−4, 4) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  33. 33.What is the midpoint of the line joining (2, 11) and (10, 1)? (a) (4, 5) (b) (12, 12) (c) (7, 6) (d) (6, 6)
  34. 34.What is the midpoint of the line joining (8, 16) and (14, 6)? (a) (22, 22) (b) (3, 5) (c) (12, 11) (d) (11, 11)
  35. 35.What is the distance between the points (5, 0) and (9, 3)? (a) 7 (b) 5 (c) 6 (d) 25
  36. 36.In which quadrant does the point (5, −4) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  37. 37.In which quadrant does the point (7, 3) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  38. 38.What is the midpoint of the line joining (6, 13) and (8, 5)? (a) (7, 9) (b) (14, 18) (c) (1, 4) (d) (9, 7)
  39. 39.In which quadrant does the point (3, −5) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  40. 40.What is the midpoint of the line joining (9, 17) and (21, 5)? (a) (11, 15) (b) (30, 22) (c) (6, 6) (d) (15, 11)

Answer key

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

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