← Coordinates and distance lesson New set →

Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 723 · 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 (9, 3) and (21, 8)? (a) 13 (b) 14 (c) 169 (d) 17
  2. 2.What is the distance between the points (6, 3) and (15, 15)? (a) 21 (b) 225 (c) 15 (d) 16
  3. 3.In which quadrant does the point (2, 6) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  4. 4.What is the distance between the points (9, 5) and (16, 29)? (a) 25 (b) 31 (c) 625 (d) 26
  5. 5.What is the distance between the points (4, 8) and (7, 12)? (a) 25 (b) 5 (c) 7 (d) 6
  6. 6.What is the distance between the points (2, 16) and (7, 4)? (a) 13 (b) 17 (c) 14 (d) 169
  7. 7.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 20 (c) 400 (d) 21
  8. 8.What is the distance between the points (5, 4) and (10, 16)? (a) 17 (b) 13 (c) 14 (d) 169
  9. 9.What is the midpoint of the line joining (8, 12) and (14, 0)? (a) (22, 12) (b) (3, 6) (c) (6, 11) (d) (11, 6)
  10. 10.In which quadrant does the point (−5, 4) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  11. 11.In which quadrant does the point (2, −3) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  12. 12.What is the midpoint of the line joining (3, 12) and (11, 0)? (a) (4, 6) (b) (7, 6) (c) (6, 7) (d) (14, 12)
  13. 13.What is the distance between the points (0, 8) and (8, 2)? (a) 100 (b) 14 (c) 11 (d) 10
  14. 14.What is the distance between the points (5, 0) and (12, 24)? (a) 625 (b) 25 (c) 31 (d) 26
  15. 15.What is the distance between the points (6, 2) and (12, 10)? (a) 14 (b) 11 (c) 100 (d) 10
  16. 16.In which quadrant does the point (−8, −3) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  17. 17.What is the distance between the points (2, 13) and (7, 1)? (a) 14 (b) 169 (c) 17 (d) 13
  18. 18.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 26 (c) 31 (d) 25
  19. 19.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 225 (c) 16 (d) 15
  20. 20.What is the distance between the points (3, 2) and (18, 10)? (a) 18 (b) 17 (c) 289 (d) 23
  21. 21.What is the distance between the points (7, 9) and (31, 16)? (a) 31 (b) 26 (c) 25 (d) 625
  22. 22.What is the distance between the points (5, 7) and (9, 4)? (a) 6 (b) 5 (c) 7 (d) 25
  23. 23.How far is the point (12, 9) from the origin (0, 0)? (a) 15 (b) 21 (c) 16 (d) 225
  24. 24.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 18 (c) 289 (d) 23
  25. 25.What is the midpoint of the line joining (7, 7) and (19, 1)? (a) (4, 13) (b) (13, 4) (c) (26, 8) (d) (6, 3)
  26. 26.What is the distance between the points (6, 16) and (18, 7)? (a) 15 (b) 16 (c) 21 (d) 225
  27. 27.In which quadrant does the point (6, 9) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  28. 28.What is the distance between the points (2, 11) and (5, 7)? (a) 6 (b) 7 (c) 25 (d) 5
  29. 29.What is the distance between the points (0, 2) and (8, 8)? (a) 11 (b) 10 (c) 100 (d) 14
  30. 30.What is the distance between the points (5, 1) and (8, 5)? (a) 6 (b) 5 (c) 7 (d) 25
  31. 31.What is the midpoint of the line joining (5, 11) and (9, 1)? (a) (6, 7) (b) (2, 5) (c) (7, 6) (d) (14, 12)
  32. 32.What is the distance between the points (5, 21) and (14, 9)? (a) 15 (b) 21 (c) 225 (d) 16
  33. 33.What is the distance between the points (5, 2) and (9, 5)? (a) 6 (b) 25 (c) 7 (d) 5
  34. 34.What is the distance between the points (3, 8) and (18, 16)? (a) 289 (b) 18 (c) 23 (d) 17
  35. 35.What is the distance between the points (6, 16) and (15, 4)? (a) 15 (b) 225 (c) 21 (d) 16
  36. 36.What is the distance between the points (9, 0) and (21, 16)? (a) 21 (b) 400 (c) 28 (d) 20
  37. 37.What is the midpoint of the line joining (9, 11) and (15, 3)? (a) (3, 4) (b) (24, 14) (c) (7, 12) (d) (12, 7)
  38. 38.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 6 (c) 7 (d) 5
  39. 39.What is the distance between the points (6, 10) and (18, 1)? (a) 21 (b) 225 (c) 15 (d) 16
  40. 40.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 10 (c) 14 (d) 100

Answer key

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

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