← Coordinates and distance lesson New set →

Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 433 · 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.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 225 (c) 21 (d) 15
  2. 2.What is the distance between the points (8, 16) and (20, 0)? (a) 400 (b) 20 (c) 28 (d) 21
  3. 3.What is the distance between the points (1, 2) and (13, 7)? (a) 17 (b) 14 (c) 169 (d) 13
  4. 4.What is the midpoint of the line joining (5, 0) and (11, 2)? (a) (8, 1) (b) (1, 8) (c) (3, 1) (d) (16, 2)
  5. 5.In which quadrant does the point (7, 3) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  6. 6.What is the distance between the points (4, 11) and (19, 3)? (a) 18 (b) 289 (c) 17 (d) 23
  7. 7.What is the distance between the points (4, 3) and (11, 27)? (a) 25 (b) 625 (c) 26 (d) 31
  8. 8.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 17 (c) 23 (d) 289
  9. 9.What is the distance between the points (8, 3) and (15, 27)? (a) 625 (b) 31 (c) 26 (d) 25
  10. 10.What is the midpoint of the line joining (8, 2) and (16, 10)? (a) (4, 4) (b) (12, 6) (c) (24, 12) (d) (6, 12)
  11. 11.In which quadrant does the point (8, −3) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  12. 12.In which quadrant does the point (−2, −7) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  13. 13.In which quadrant does the point (1, 4) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  14. 14.What is the midpoint of the line joining (6, 8) and (10, 6)? (a) (7, 8) (b) (2, 1) (c) (8, 7) (d) (16, 14)
  15. 15.In which quadrant does the point (−7, −4) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  16. 16.What is the distance between the points (4, 1) and (10, 9)? (a) 11 (b) 14 (c) 100 (d) 10
  17. 17.What is the distance between the points (7, 14) and (31, 7)? (a) 25 (b) 26 (c) 31 (d) 625
  18. 18.What is the midpoint of the line joining (1, 1) and (5, 3)? (a) (6, 4) (b) (2, 3) (c) (3, 2) (d) (2, 1)
  19. 19.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 7 (c) 6 (d) 5
  20. 20.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 14 (c) 10 (d) 11
  21. 21.What is the midpoint of the line joining (4, 8) and (10, 2)? (a) (3, 3) (b) (7, 5) (c) (5, 7) (d) (14, 10)
  22. 22.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 31 (c) 25 (d) 26
  23. 23.What is the midpoint of the line joining (3, 2) and (5, 6)? (a) (1, 2) (b) (5, 4) (c) (8, 8) (d) (4, 4)
  24. 24.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 28 (c) 400 (d) 20
  25. 25.What is the midpoint of the line joining (1, 6) and (5, 8)? (a) (7, 3) (b) (3, 7) (c) (2, 1) (d) (6, 14)
  26. 26.What is the midpoint of the line joining (7, 13) and (9, 7)? (a) (10, 8) (b) (1, 3) (c) (16, 20) (d) (8, 10)
  27. 27.What is the distance between the points (5, 4) and (9, 7)? (a) 7 (b) 25 (c) 6 (d) 5
  28. 28.What is the distance between the points (1, 9) and (5, 6)? (a) 5 (b) 25 (c) 6 (d) 7
  29. 29.What is the distance between the points (5, 20) and (14, 8)? (a) 225 (b) 21 (c) 16 (d) 15
  30. 30.In which quadrant does the point (−8, 9) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  31. 31.In which quadrant does the point (−1, −8) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  32. 32.What is the distance between the points (0, 1) and (5, 13)? (a) 169 (b) 17 (c) 14 (d) 13
  33. 33.In which quadrant does the point (−9, −4) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  34. 34.In which quadrant does the point (−4, 6) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  35. 35.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 16 (c) 15 (d) 225
  36. 36.What is the midpoint of the line joining (5, 8) and (15, 10)? (a) (9, 10) (b) (5, 1) (c) (10, 9) (d) (20, 18)
  37. 37.What is the midpoint of the line joining (1, 10) and (3, 22)? (a) (4, 32) (b) (16, 2) (c) (1, 6) (d) (2, 16)
  38. 38.What is the midpoint of the line joining (8, 4) and (20, 10)? (a) (28, 14) (b) (7, 14) (c) (6, 3) (d) (14, 7)
  39. 39.What is the midpoint of the line joining (0, 10) and (8, 22)? (a) (4, 6) (b) (4, 16) (c) (8, 32) (d) (16, 4)
  40. 40.In which quadrant does the point (−8, 3) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant

Answer key

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

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