← Coordinates and distance lesson New set →

Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 510 · 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 (6, 2) and (10, 14)? (a) (16, 16) (b) (2, 6) (c) (8, 8) (d) (9, 8)
  2. 2.What is the distance between the points (4, 6) and (8, 9)? (a) 7 (b) 5 (c) 25 (d) 6
  3. 3.How far is the point (24, 7) from the origin (0, 0)? (a) 26 (b) 25 (c) 31 (d) 625
  4. 4.What is the distance between the points (4, 8) and (16, 13)? (a) 17 (b) 13 (c) 14 (d) 169
  5. 5.What is the midpoint of the line joining (6, 1) and (16, 5)? (a) (22, 6) (b) (3, 11) (c) (5, 2) (d) (11, 3)
  6. 6.What is the distance between the points (7, 20) and (15, 5)? (a) 17 (b) 23 (c) 289 (d) 18
  7. 7.In which quadrant does the point (−1, 6) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  8. 8.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 6 (c) 7 (d) 5
  9. 9.In which quadrant does the point (4, −8) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  10. 10.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 7 (c) 25 (d) 6
  11. 11.What is the distance between the points (0, 13) and (8, 7)? (a) 14 (b) 100 (c) 10 (d) 11
  12. 12.How far is the point (12, 16) from the origin (0, 0)? (a) 20 (b) 21 (c) 28 (d) 400
  13. 13.What is the distance between the points (4, 2) and (11, 26)? (a) 25 (b) 31 (c) 26 (d) 625
  14. 14.What is the distance between the points (7, 1) and (15, 7)? (a) 14 (b) 10 (c) 11 (d) 100
  15. 15.In which quadrant does the point (2, −7) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  16. 16.What is the midpoint of the line joining (1, 21) and (5, 9)? (a) (6, 30) (b) (2, 6) (c) (15, 3) (d) (3, 15)
  17. 17.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 17 (c) 289 (d) 18
  18. 18.What is the midpoint of the line joining (3, 9) and (5, 21)? (a) (15, 4) (b) (4, 15) (c) (1, 6) (d) (8, 30)
  19. 19.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 28 (c) 400 (d) 21
  20. 20.What is the distance between the points (2, 11) and (5, 7)? (a) 6 (b) 7 (c) 5 (d) 25
  21. 21.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 15 (c) 21 (d) 16
  22. 22.What is the midpoint of the line joining (5, 6) and (7, 10)? (a) (6, 8) (b) (12, 16) (c) (1, 2) (d) (8, 6)
  23. 23.What is the distance between the points (4, 15) and (20, 3)? (a) 20 (b) 400 (c) 21 (d) 28
  24. 24.What is the distance between the points (0, 7) and (5, 19)? (a) 17 (b) 169 (c) 13 (d) 14
  25. 25.In which quadrant does the point (7, 9) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  26. 26.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 14 (c) 10 (d) 100
  27. 27.What is the midpoint of the line joining (4, 10) and (12, 14)? (a) (16, 24) (b) (8, 12) (c) (4, 2) (d) (12, 8)
  28. 28.What is the distance between the points (1, 7) and (13, 23)? (a) 21 (b) 400 (c) 28 (d) 20
  29. 29.In which quadrant does the point (−1, −4) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  30. 30.What is the midpoint of the line joining (10, 3) and (14, 9)? (a) (6, 12) (b) (2, 3) (c) (24, 12) (d) (12, 6)
  31. 31.In which quadrant does the point (−6, 4) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  32. 32.What is the midpoint of the line joining (1, 9) and (7, 13)? (a) (11, 4) (b) (8, 22) (c) (4, 11) (d) (3, 2)
  33. 33.What is the midpoint of the line joining (3, 8) and (13, 2)? (a) (5, 8) (b) (5, 3) (c) (8, 5) (d) (16, 10)
  34. 34.In which quadrant does the point (6, −6) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  35. 35.What is the distance between the points (8, 7) and (32, 0)? (a) 26 (b) 25 (c) 31 (d) 625
  36. 36.What is the midpoint of the line joining (0, 9) and (6, 1)? (a) (3, 4) (b) (5, 3) (c) (3, 5) (d) (6, 10)
  37. 37.What is the midpoint of the line joining (1, 7) and (13, 5)? (a) (6, 7) (b) (6, 1) (c) (7, 6) (d) (14, 12)
  38. 38.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 100 (c) 10 (d) 11
  39. 39.What is the distance between the points (5, 1) and (13, 7)? (a) 14 (b) 11 (c) 10 (d) 100
  40. 40.In which quadrant does the point (−9, −3) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant

Answer key

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

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