← Coordinates and distance lesson New set →

Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 414 · 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 (5, 11) and (11, 1)? (a) (3, 5) (b) (8, 6) (c) (16, 12) (d) (6, 8)
  2. 2.In which quadrant does the point (−4, −5) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  3. 3.What is the distance between the points (0, 7) and (4, 4)? (a) 5 (b) 7 (c) 25 (d) 6
  4. 4.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 25 (c) 5 (d) 7
  5. 5.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 169 (c) 13 (d) 17
  6. 6.What is the midpoint of the line joining (4, 16) and (16, 4)? (a) (6, 6) (b) (20, 20) (c) (11, 10) (d) (10, 10)
  7. 7.What is the midpoint of the line joining (6, 11) and (8, 7)? (a) (7, 9) (b) (1, 2) (c) (14, 18) (d) (9, 7)
  8. 8.What is the distance between the points (1, 3) and (7, 11)? (a) 14 (b) 10 (c) 100 (d) 11
  9. 9.What is the midpoint of the line joining (10, 5) and (12, 9)? (a) (22, 14) (b) (1, 2) (c) (7, 11) (d) (11, 7)
  10. 10.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 26 (c) 25 (d) 31
  11. 11.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 14 (c) 17 (d) 13
  12. 12.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 400 (c) 20 (d) 21
  13. 13.What is the distance between the points (4, 9) and (19, 1)? (a) 18 (b) 289 (c) 17 (d) 23
  14. 14.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 11 (c) 14 (d) 100
  15. 15.In which quadrant does the point (2, 9) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  16. 16.In which quadrant does the point (−7, 7) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  17. 17.In which quadrant does the point (5, 6) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  18. 18.In which quadrant does the point (−3, −1) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  19. 19.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 225 (c) 16 (d) 15
  20. 20.What is the midpoint of the line joining (4, 1) and (16, 5)? (a) (20, 6) (b) (3, 10) (c) (6, 2) (d) (10, 3)
  21. 21.In which quadrant does the point (−7, 9) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  22. 22.What is the distance between the points (1, 20) and (10, 8)? (a) 225 (b) 21 (c) 16 (d) 15
  23. 23.In which quadrant does the point (−7, −4) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  24. 24.What is the distance between the points (0, 5) and (3, 1)? (a) 25 (b) 6 (c) 7 (d) 5
  25. 25.What is the midpoint of the line joining (6, 13) and (12, 5)? (a) (9, 9) (b) (18, 18) (c) (10, 9) (d) (3, 4)
  26. 26.What is the midpoint of the line joining (6, 3) and (12, 11)? (a) (18, 14) (b) (9, 7) (c) (3, 4) (d) (7, 9)
  27. 27.In which quadrant does the point (−7, 6) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  28. 28.In which quadrant does the point (−2, 6) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  29. 29.What is the midpoint of the line joining (2, 8) and (10, 18)? (a) (4, 5) (b) (6, 13) (c) (13, 6) (d) (12, 26)
  30. 30.In which quadrant does the point (4, −3) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  31. 31.What is the distance between the points (1, 10) and (5, 7)? (a) 6 (b) 25 (c) 5 (d) 7
  32. 32.In which quadrant does the point (3, −8) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  33. 33.What is the midpoint of the line joining (6, 20) and (18, 8)? (a) (12, 14) (b) (24, 28) (c) (14, 12) (d) (6, 6)
  34. 34.In which quadrant does the point (−1, −8) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  35. 35.In which quadrant does the point (−2, −4) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  36. 36.What is the midpoint of the line joining (5, 3) and (17, 1)? (a) (11, 2) (b) (6, 1) (c) (22, 4) (d) (2, 11)
  37. 37.In which quadrant does the point (6, −4) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  38. 38.What is the midpoint of the line joining (8, 14) and (12, 8)? (a) (10, 11) (b) (11, 10) (c) (20, 22) (d) (2, 3)
  39. 39.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 15 (c) 225 (d) 16
  40. 40.What is the distance between the points (3, 2) and (11, 17)? (a) 17 (b) 18 (c) 289 (d) 23

Answer key

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

Free maths olympiad lessons, practice and worksheets at talentjr.in/maths-olympiad