← Coordinates and distance lesson New set →

Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 75 · 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 (6, 2) and (12, 10)? (a) 100 (b) 10 (c) 11 (d) 14
  2. 2.How far is the point (7, 24) from the origin (0, 0)? (a) 25 (b) 31 (c) 625 (d) 26
  3. 3.What is the midpoint of the line joining (9, 13) and (17, 9)? (a) (4, 2) (b) (13, 11) (c) (26, 22) (d) (11, 13)
  4. 4.What is the midpoint of the line joining (3, 1) and (15, 3)? (a) (2, 9) (b) (6, 1) (c) (9, 2) (d) (18, 4)
  5. 5.In which quadrant does the point (−7, −4) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  6. 6.In which quadrant does the point (−9, −9) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  7. 7.What is the distance between the points (0, 6) and (12, 11)? (a) 14 (b) 169 (c) 17 (d) 13
  8. 8.In which quadrant does the point (−4, 5) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  9. 9.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 7 (c) 6 (d) 25
  10. 10.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 7 (c) 5 (d) 6
  11. 11.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 14 (c) 10 (d) 11
  12. 12.What is the midpoint of the line joining (10, 5) and (22, 7)? (a) (32, 12) (b) (16, 6) (c) (6, 1) (d) (6, 16)
  13. 13.What is the distance between the points (5, 8) and (11, 16)? (a) 100 (b) 14 (c) 10 (d) 11
  14. 14.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 26 (c) 25 (d) 31
  15. 15.What is the midpoint of the line joining (2, 14) and (8, 4)? (a) (5, 9) (b) (10, 18) (c) (9, 5) (d) (3, 5)
  16. 16.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 10 (c) 14 (d) 100
  17. 17.What is the distance between the points (3, 2) and (6, 6)? (a) 6 (b) 5 (c) 25 (d) 7
  18. 18.What is the distance between the points (1, 14) and (6, 2)? (a) 169 (b) 14 (c) 17 (d) 13
  19. 19.What is the distance between the points (0, 11) and (6, 3)? (a) 11 (b) 14 (c) 10 (d) 100
  20. 20.What is the midpoint of the line joining (2, 4) and (8, 10)? (a) (7, 5) (b) (5, 7) (c) (10, 14) (d) (3, 3)
  21. 21.In which quadrant does the point (4, −4) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  22. 22.What is the distance between the points (6, 18) and (11, 6)? (a) 169 (b) 13 (c) 17 (d) 14
  23. 23.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 17 (c) 14 (d) 13
  24. 24.What is the distance between the points (1, 3) and (9, 9)? (a) 100 (b) 10 (c) 11 (d) 14
  25. 25.What is the distance between the points (9, 18) and (18, 6)? (a) 15 (b) 21 (c) 16 (d) 225
  26. 26.What is the distance between the points (0, 9) and (6, 1)? (a) 14 (b) 11 (c) 10 (d) 100
  27. 27.In which quadrant does the point (−1, −6) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  28. 28.What is the distance between the points (0, 23) and (8, 8)? (a) 23 (b) 289 (c) 18 (d) 17
  29. 29.What is the midpoint of the line joining (0, 2) and (4, 4)? (a) (3, 2) (b) (4, 6) (c) (2, 1) (d) (2, 3)
  30. 30.In which quadrant does the point (3, 5) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  31. 31.What is the distance between the points (4, 4) and (10, 12)? (a) 11 (b) 10 (c) 100 (d) 14
  32. 32.What is the distance between the points (3, 3) and (15, 12)? (a) 21 (b) 225 (c) 16 (d) 15
  33. 33.In which quadrant does the point (7, 1) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  34. 34.In which quadrant does the point (−6, 9) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  35. 35.What is the distance between the points (6, 2) and (18, 11)? (a) 21 (b) 16 (c) 225 (d) 15
  36. 36.In which quadrant does the point (−3, 4) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  37. 37.How far is the point (12, 16) from the origin (0, 0)? (a) 20 (b) 28 (c) 21 (d) 400
  38. 38.In which quadrant does the point (5, 8) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  39. 39.In which quadrant does the point (−7, 5) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  40. 40.What is the distance between the points (4, 7) and (28, 0)? (a) 625 (b) 31 (c) 26 (d) 25

Answer key

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

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