← Coordinates and distance lesson New set →

Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 388 · 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, 10) and (24, 2)? (a) 23 (b) 289 (c) 17 (d) 18
  2. 2.What is the distance between the points (3, 0) and (15, 5)? (a) 169 (b) 14 (c) 17 (d) 13
  3. 3.What is the distance between the points (2, 2) and (14, 11)? (a) 16 (b) 21 (c) 15 (d) 225
  4. 4.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 17 (c) 23 (d) 289
  5. 5.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 31 (c) 25 (d) 26
  6. 6.How far is the point (4, 3) from the origin (0, 0)? (a) 5 (b) 6 (c) 7 (d) 25
  7. 7.What is the distance between the points (3, 7) and (9, 15)? (a) 10 (b) 14 (c) 100 (d) 11
  8. 8.In which quadrant does the point (−2, −2) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  9. 9.What is the midpoint of the line joining (1, 8) and (3, 2)? (a) (5, 2) (b) (1, 3) (c) (4, 10) (d) (2, 5)
  10. 10.In which quadrant does the point (3, −4) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  11. 11.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 17 (c) 169 (d) 13
  12. 12.What is the distance between the points (9, 14) and (24, 6)? (a) 18 (b) 23 (c) 17 (d) 289
  13. 13.What is the distance between the points (6, 17) and (18, 1)? (a) 28 (b) 400 (c) 20 (d) 21
  14. 14.What is the midpoint of the line joining (10, 18) and (14, 8)? (a) (24, 26) (b) (12, 13) (c) (13, 12) (d) (2, 5)
  15. 15.In which quadrant does the point (−2, 9) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  16. 16.What is the midpoint of the line joining (5, 1) and (7, 13)? (a) (7, 6) (b) (6, 7) (c) (1, 6) (d) (12, 14)
  17. 17.What is the midpoint of the line joining (6, 4) and (12, 16)? (a) (18, 20) (b) (9, 10) (c) (10, 9) (d) (3, 6)
  18. 18.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 5 (c) 25 (d) 7
  19. 19.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 20 (c) 400 (d) 21
  20. 20.In which quadrant does the point (6, −5) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  21. 21.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 14 (c) 11 (d) 100
  22. 22.In which quadrant does the point (5, 1) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  23. 23.What is the distance between the points (9, 8) and (12, 4)? (a) 5 (b) 25 (c) 6 (d) 7
  24. 24.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 18 (c) 23 (d) 17
  25. 25.In which quadrant does the point (3, 6) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  26. 26.In which quadrant does the point (8, 4) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  27. 27.What is the distance between the points (9, 2) and (18, 14)? (a) 15 (b) 16 (c) 21 (d) 225
  28. 28.In which quadrant does the point (−2, −3) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  29. 29.What is the distance between the points (9, 5) and (25, 17)? (a) 28 (b) 400 (c) 20 (d) 21
  30. 30.What is the distance between the points (3, 2) and (12, 14)? (a) 15 (b) 16 (c) 21 (d) 225
  31. 31.What is the distance between the points (9, 4) and (33, 11)? (a) 25 (b) 625 (c) 31 (d) 26
  32. 32.What is the midpoint of the line joining (0, 7) and (2, 5)? (a) (2, 12) (b) (1, 1) (c) (1, 6) (d) (6, 1)
  33. 33.What is the distance between the points (9, 14) and (14, 2)? (a) 14 (b) 17 (c) 13 (d) 169
  34. 34.In which quadrant does the point (−3, 4) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  35. 35.What is the midpoint of the line joining (1, 21) and (3, 9)? (a) (1, 6) (b) (4, 30) (c) (15, 2) (d) (2, 15)
  36. 36.What is the distance between the points (8, 11) and (12, 8)? (a) 7 (b) 25 (c) 6 (d) 5
  37. 37.What is the distance between the points (6, 1) and (9, 5)? (a) 7 (b) 6 (c) 5 (d) 25
  38. 38.What is the distance between the points (4, 9) and (20, 21)? (a) 21 (b) 400 (c) 20 (d) 28
  39. 39.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 21 (c) 15 (d) 16
  40. 40.In which quadrant does the point (2, 5) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant

Answer key

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

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