← Coordinates and distance lesson New set →

Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 495 · 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 (9, 5) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  2. 2.What is the distance between the points (5, 15) and (11, 7)? (a) 10 (b) 11 (c) 100 (d) 14
  3. 3.What is the distance between the points (8, 4) and (17, 16)? (a) 21 (b) 16 (c) 225 (d) 15
  4. 4.What is the midpoint of the line joining (2, 2) and (4, 8)? (a) (5, 3) (b) (6, 10) (c) (1, 3) (d) (3, 5)
  5. 5.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 25 (c) 6 (d) 5
  6. 6.In which quadrant does the point (−9, 4) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  7. 7.What is the midpoint of the line joining (4, 1) and (14, 3)? (a) (5, 1) (b) (9, 2) (c) (18, 4) (d) (2, 9)
  8. 8.What is the midpoint of the line joining (0, 6) and (6, 18)? (a) (3, 12) (b) (12, 3) (c) (3, 6) (d) (6, 24)
  9. 9.What is the midpoint of the line joining (8, 6) and (16, 16)? (a) (11, 12) (b) (4, 5) (c) (12, 11) (d) (24, 22)
  10. 10.What is the distance between the points (5, 8) and (29, 1)? (a) 625 (b) 31 (c) 26 (d) 25
  11. 11.What is the midpoint of the line joining (7, 8) and (13, 12)? (a) (20, 20) (b) (11, 10) (c) (3, 2) (d) (10, 10)
  12. 12.In which quadrant does the point (2, 5) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  13. 13.What is the midpoint of the line joining (2, 9) and (8, 1)? (a) (5, 5) (b) (10, 10) (c) (6, 5) (d) (3, 4)
  14. 14.What is the distance between the points (0, 17) and (9, 5)? (a) 21 (b) 16 (c) 15 (d) 225
  15. 15.What is the midpoint of the line joining (3, 7) and (15, 1)? (a) (9, 4) (b) (4, 9) (c) (18, 8) (d) (6, 3)
  16. 16.In which quadrant does the point (5, 3) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  17. 17.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 225 (c) 16 (d) 15
  18. 18.In which quadrant does the point (8, −2) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  19. 19.What is the distance between the points (3, 0) and (10, 24)? (a) 625 (b) 26 (c) 25 (d) 31
  20. 20.In which quadrant does the point (2, −9) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  21. 21.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 31 (c) 25 (d) 625
  22. 22.What is the midpoint of the line joining (8, 0) and (12, 12)? (a) (20, 12) (b) (6, 10) (c) (10, 6) (d) (2, 6)
  23. 23.What is the distance between the points (2, 0) and (5, 4)? (a) 7 (b) 25 (c) 6 (d) 5
  24. 24.What is the midpoint of the line joining (9, 5) and (13, 1)? (a) (11, 3) (b) (3, 11) (c) (22, 6) (d) (2, 2)
  25. 25.In which quadrant does the point (−8, −8) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  26. 26.In which quadrant does the point (3, 5) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  27. 27.What is the midpoint of the line joining (4, 3) and (6, 13)? (a) (8, 5) (b) (10, 16) (c) (1, 5) (d) (5, 8)
  28. 28.What is the midpoint of the line joining (3, 22) and (5, 10)? (a) (1, 6) (b) (8, 32) (c) (4, 16) (d) (16, 4)
  29. 29.What is the distance between the points (1, 7) and (4, 11)? (a) 7 (b) 5 (c) 25 (d) 6
  30. 30.What is the midpoint of the line joining (7, 3) and (11, 9)? (a) (2, 3) (b) (9, 6) (c) (18, 12) (d) (6, 9)
  31. 31.What is the distance between the points (1, 24) and (8, 0)? (a) 25 (b) 26 (c) 625 (d) 31
  32. 32.In which quadrant does the point (−5, 1) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  33. 33.In which quadrant does the point (4, 8) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  34. 34.What is the midpoint of the line joining (7, 1) and (17, 3)? (a) (2, 12) (b) (24, 4) (c) (12, 2) (d) (5, 1)
  35. 35.In which quadrant does the point (1, 9) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  36. 36.In which quadrant does the point (−6, −9) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  37. 37.What is the distance between the points (4, 15) and (12, 0)? (a) 18 (b) 289 (c) 17 (d) 23
  38. 38.How far is the point (24, 7) from the origin (0, 0)? (a) 26 (b) 31 (c) 625 (d) 25
  39. 39.In which quadrant does the point (−5, 4) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  40. 40.In which quadrant does the point (−1, 6) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant

Answer key

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

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