← Coordinates and distance lesson New set →

Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 324 · 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, −9) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  2. 2.What is the midpoint of the line joining (4, 4) and (8, 12)? (a) (8, 6) (b) (6, 8) (c) (12, 16) (d) (2, 4)
  3. 3.What is the midpoint of the line joining (6, 10) and (10, 2)? (a) (8, 6) (b) (16, 12) (c) (2, 4) (d) (6, 8)
  4. 4.What is the midpoint of the line joining (3, 8) and (15, 14)? (a) (9, 11) (b) (18, 22) (c) (11, 9) (d) (6, 3)
  5. 5.In which quadrant does the point (8, 9) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  6. 6.In which quadrant does the point (9, −6) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  7. 7.In which quadrant does the point (7, −9) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  8. 8.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 18 (c) 289 (d) 17
  9. 9.What is the distance between the points (5, 8) and (17, 13)? (a) 13 (b) 169 (c) 14 (d) 17
  10. 10.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 31 (c) 26 (d) 25
  11. 11.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 225 (c) 16 (d) 15
  12. 12.In which quadrant does the point (−4, −1) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  13. 13.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 15 (c) 225 (d) 16
  14. 14.In which quadrant does the point (−3, 8) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  15. 15.In which quadrant does the point (−6, −8) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  16. 16.In which quadrant does the point (−5, 2) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  17. 17.What is the distance between the points (5, 13) and (29, 6)? (a) 25 (b) 26 (c) 625 (d) 31
  18. 18.What is the distance between the points (5, 5) and (11, 13)? (a) 11 (b) 10 (c) 100 (d) 14
  19. 19.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 17 (c) 289 (d) 23
  20. 20.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 13 (c) 17 (d) 169
  21. 21.What is the distance between the points (7, 12) and (19, 3)? (a) 21 (b) 16 (c) 225 (d) 15
  22. 22.What is the distance between the points (8, 11) and (11, 7)? (a) 25 (b) 6 (c) 5 (d) 7
  23. 23.What is the midpoint of the line joining (2, 13) and (14, 3)? (a) (8, 8) (b) (6, 5) (c) (9, 8) (d) (16, 16)
  24. 24.What is the distance between the points (2, 16) and (11, 4)? (a) 225 (b) 21 (c) 16 (d) 15
  25. 25.What is the distance between the points (7, 17) and (19, 1)? (a) 400 (b) 28 (c) 21 (d) 20
  26. 26.What is the midpoint of the line joining (2, 6) and (6, 10)? (a) (8, 4) (b) (8, 16) (c) (2, 2) (d) (4, 8)
  27. 27.In which quadrant does the point (−3, −2) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  28. 28.What is the distance between the points (9, 3) and (12, 7)? (a) 25 (b) 7 (c) 5 (d) 6
  29. 29.What is the distance between the points (5, 12) and (9, 9)? (a) 6 (b) 7 (c) 25 (d) 5
  30. 30.What is the midpoint of the line joining (9, 8) and (19, 4)? (a) (14, 6) (b) (5, 2) (c) (6, 14) (d) (28, 12)
  31. 31.What is the distance between the points (4, 19) and (9, 7)? (a) 13 (b) 17 (c) 14 (d) 169
  32. 32.In which quadrant does the point (−8, −1) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  33. 33.What is the midpoint of the line joining (2, 6) and (10, 2)? (a) (4, 6) (b) (4, 2) (c) (6, 4) (d) (12, 8)
  34. 34.What is the midpoint of the line joining (9, 10) and (19, 16)? (a) (5, 3) (b) (14, 13) (c) (13, 14) (d) (28, 26)
  35. 35.What is the distance between the points (4, 1) and (10, 9)? (a) 100 (b) 11 (c) 14 (d) 10
  36. 36.What is the distance between the points (9, 2) and (13, 5)? (a) 6 (b) 7 (c) 5 (d) 25
  37. 37.What is the distance between the points (0, 8) and (3, 12)? (a) 7 (b) 25 (c) 6 (d) 5
  38. 38.What is the distance between the points (7, 4) and (19, 13)? (a) 15 (b) 225 (c) 21 (d) 16
  39. 39.What is the distance between the points (7, 15) and (15, 0)? (a) 289 (b) 17 (c) 23 (d) 18
  40. 40.In which quadrant does the point (1, −4) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant

Answer key

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

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