← Coordinates and distance lesson New set →

Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 67 · 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 distance between the points (8, 5) and (32, 12)? (a) 26 (b) 625 (c) 31 (d) 25
  2. 2.In which quadrant does the point (3, 5) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  3. 3.In which quadrant does the point (−5, −9) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  4. 4.What is the distance between the points (7, 32) and (14, 8)? (a) 31 (b) 25 (c) 625 (d) 26
  5. 5.What is the midpoint of the line joining (10, 4) and (20, 0)? (a) (30, 4) (b) (2, 15) (c) (15, 2) (d) (5, 2)
  6. 6.What is the distance between the points (3, 9) and (9, 17)? (a) 10 (b) 100 (c) 11 (d) 14
  7. 7.What is the distance between the points (4, 21) and (13, 9)? (a) 225 (b) 16 (c) 21 (d) 15
  8. 8.How far is the point (5, 12) from the origin (0, 0)? (a) 13 (b) 14 (c) 169 (d) 17
  9. 9.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 25 (c) 5 (d) 6
  10. 10.What is the distance between the points (1, 8) and (25, 15)? (a) 25 (b) 625 (c) 31 (d) 26
  11. 11.How far is the point (24, 7) from the origin (0, 0)? (a) 26 (b) 25 (c) 625 (d) 31
  12. 12.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 7 (c) 5 (d) 25
  13. 13.What is the distance between the points (7, 15) and (19, 6)? (a) 225 (b) 15 (c) 16 (d) 21
  14. 14.What is the distance between the points (8, 9) and (17, 21)? (a) 15 (b) 16 (c) 225 (d) 21
  15. 15.In which quadrant does the point (2, 8) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  16. 16.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 14 (c) 13 (d) 169
  17. 17.What is the distance between the points (3, 14) and (9, 6)? (a) 10 (b) 100 (c) 11 (d) 14
  18. 18.What is the distance between the points (1, 7) and (13, 23)? (a) 28 (b) 21 (c) 400 (d) 20
  19. 19.In which quadrant does the point (8, 3) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  20. 20.In which quadrant does the point (9, 3) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  21. 21.What is the distance between the points (7, 1) and (16, 13)? (a) 225 (b) 15 (c) 21 (d) 16
  22. 22.What is the distance between the points (5, 0) and (13, 6)? (a) 100 (b) 11 (c) 10 (d) 14
  23. 23.In which quadrant does the point (4, −9) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  24. 24.What is the distance between the points (9, 0) and (21, 5)? (a) 17 (b) 13 (c) 14 (d) 169
  25. 25.In which quadrant does the point (1, −1) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  26. 26.In which quadrant does the point (−1, −3) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  27. 27.In which quadrant does the point (6, −5) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  28. 28.What is the midpoint of the line joining (5, 8) and (17, 20)? (a) (22, 28) (b) (6, 6) (c) (11, 14) (d) (14, 11)
  29. 29.In which quadrant does the point (4, −7) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  30. 30.What is the distance between the points (1, 8) and (16, 0)? (a) 23 (b) 289 (c) 18 (d) 17
  31. 31.What is the distance between the points (3, 2) and (11, 17)? (a) 17 (b) 289 (c) 18 (d) 23
  32. 32.In which quadrant does the point (−9, −5) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  33. 33.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 11 (c) 14 (d) 100
  34. 34.What is the midpoint of the line joining (2, 6) and (10, 12)? (a) (4, 3) (b) (6, 9) (c) (12, 18) (d) (9, 6)
  35. 35.In which quadrant does the point (−2, 4) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  36. 36.What is the distance between the points (9, 2) and (13, 5)? (a) 7 (b) 25 (c) 5 (d) 6
  37. 37.In which quadrant does the point (−9, 6) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  38. 38.What is the distance between the points (9, 8) and (12, 4)? (a) 25 (b) 6 (c) 5 (d) 7
  39. 39.In which quadrant does the point (2, 2) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  40. 40.What is the midpoint of the line joining (10, 3) and (12, 1)? (a) (11, 2) (b) (22, 4) (c) (2, 11) (d) (1, 1)

Answer key

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

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