← Coordinates and distance lesson New set →

Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 92 · 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 (8, 2) and (12, 4)? (a) (20, 6) (b) (10, 3) (c) (2, 1) (d) (3, 10)
  2. 2.In which quadrant does the point (−5, −9) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  3. 3.In which quadrant does the point (5, 4) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  4. 4.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 225 (c) 15 (d) 21
  5. 5.What is the distance between the points (1, 5) and (17, 17)? (a) 28 (b) 400 (c) 20 (d) 21
  6. 6.What is the midpoint of the line joining (1, 14) and (13, 4)? (a) (9, 7) (b) (6, 5) (c) (7, 9) (d) (14, 18)
  7. 7.In which quadrant does the point (−2, 1) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  8. 8.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 5 (c) 25 (d) 6
  9. 9.What is the distance between the points (6, 9) and (15, 21)? (a) 21 (b) 16 (c) 15 (d) 225
  10. 10.In which quadrant does the point (−8, 4) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  11. 11.What is the distance between the points (2, 20) and (18, 8)? (a) 21 (b) 400 (c) 28 (d) 20
  12. 12.In which quadrant does the point (9, 6) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  13. 13.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 21 (c) 400 (d) 28
  14. 14.What is the midpoint of the line joining (1, 12) and (13, 0)? (a) (7, 6) (b) (6, 6) (c) (6, 7) (d) (14, 12)
  15. 15.What is the distance between the points (8, 8) and (12, 11)? (a) 6 (b) 7 (c) 5 (d) 25
  16. 16.What is the distance between the points (7, 12) and (12, 0)? (a) 14 (b) 17 (c) 13 (d) 169
  17. 17.What is the distance between the points (3, 13) and (19, 1)? (a) 400 (b) 21 (c) 28 (d) 20
  18. 18.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 100 (c) 11 (d) 10
  19. 19.In which quadrant does the point (9, −9) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  20. 20.What is the midpoint of the line joining (4, 20) and (10, 10)? (a) (15, 7) (b) (3, 5) (c) (14, 30) (d) (7, 15)
  21. 21.What is the midpoint of the line joining (1, 18) and (13, 8)? (a) (13, 7) (b) (14, 26) (c) (7, 13) (d) (6, 5)
  22. 22.In which quadrant does the point (−1, 7) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  23. 23.In which quadrant does the point (−3, −4) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  24. 24.What is the distance between the points (7, 17) and (13, 9)? (a) 100 (b) 11 (c) 10 (d) 14
  25. 25.What is the distance between the points (7, 1) and (11, 4)? (a) 25 (b) 6 (c) 7 (d) 5
  26. 26.What is the distance between the points (5, 2) and (11, 10)? (a) 11 (b) 10 (c) 100 (d) 14
  27. 27.What is the midpoint of the line joining (9, 14) and (11, 4)? (a) (10, 9) (b) (20, 18) (c) (1, 5) (d) (9, 10)
  28. 28.What is the midpoint of the line joining (0, 9) and (4, 13)? (a) (2, 11) (b) (11, 2) (c) (4, 22) (d) (2, 2)
  29. 29.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 625 (c) 31 (d) 25
  30. 30.What is the midpoint of the line joining (8, 8) and (10, 4)? (a) (18, 12) (b) (9, 6) (c) (1, 2) (d) (6, 9)
  31. 31.What is the midpoint of the line joining (1, 6) and (9, 14)? (a) (10, 20) (b) (4, 4) (c) (10, 5) (d) (5, 10)
  32. 32.In which quadrant does the point (9, −8) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  33. 33.In which quadrant does the point (6, 2) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  34. 34.In which quadrant does the point (−2, −3) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  35. 35.In which quadrant does the point (−2, −9) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  36. 36.What is the distance between the points (7, 2) and (15, 17)? (a) 17 (b) 23 (c) 18 (d) 289
  37. 37.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 25 (c) 6 (d) 5
  38. 38.What is the distance between the points (8, 24) and (15, 0)? (a) 25 (b) 625 (c) 31 (d) 26
  39. 39.What is the midpoint of the line joining (8, 8) and (10, 10)? (a) (1, 1) (b) (18, 18) (c) (10, 9) (d) (9, 9)
  40. 40.In which quadrant does the point (6, −9) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant

Answer key

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

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