← Coordinates and distance lesson New set →

Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 70 · 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 (4, 9) and (8, 12)? (a) 6 (b) 7 (c) 5 (d) 25
  2. 2.How far is the point (12, 16) from the origin (0, 0)? (a) 20 (b) 400 (c) 28 (d) 21
  3. 3.What is the midpoint of the line joining (0, 16) and (4, 4)? (a) (4, 20) (b) (10, 2) (c) (2, 10) (d) (2, 6)
  4. 4.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 289 (c) 17 (d) 18
  5. 5.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 11 (c) 100 (d) 10
  6. 6.In which quadrant does the point (5, 3) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  7. 7.What is the distance between the points (0, 14) and (24, 7)? (a) 31 (b) 26 (c) 625 (d) 25
  8. 8.In which quadrant does the point (6, 3) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  9. 9.What is the distance between the points (4, 5) and (7, 1)? (a) 7 (b) 25 (c) 6 (d) 5
  10. 10.What is the distance between the points (2, 5) and (5, 1)? (a) 25 (b) 5 (c) 6 (d) 7
  11. 11.What is the midpoint of the line joining (7, 0) and (9, 12)? (a) (1, 6) (b) (6, 8) (c) (8, 6) (d) (16, 12)
  12. 12.What is the distance between the points (6, 7) and (15, 19)? (a) 15 (b) 21 (c) 16 (d) 225
  13. 13.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 23 (c) 18 (d) 289
  14. 14.In which quadrant does the point (9, 9) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  15. 15.What is the distance between the points (9, 7) and (13, 10)? (a) 6 (b) 5 (c) 25 (d) 7
  16. 16.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 11 (c) 14 (d) 10
  17. 17.What is the midpoint of the line joining (7, 17) and (19, 7)? (a) (26, 24) (b) (6, 5) (c) (12, 13) (d) (13, 12)
  18. 18.In which quadrant does the point (5, 2) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  19. 19.What is the distance between the points (4, 5) and (16, 21)? (a) 400 (b) 20 (c) 21 (d) 28
  20. 20.What is the distance between the points (2, 9) and (6, 6)? (a) 7 (b) 5 (c) 25 (d) 6
  21. 21.What is the distance between the points (3, 8) and (7, 5)? (a) 25 (b) 6 (c) 5 (d) 7
  22. 22.In which quadrant does the point (−4, −9) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  23. 23.What is the distance between the points (1, 11) and (4, 7)? (a) 7 (b) 25 (c) 5 (d) 6
  24. 24.What is the distance between the points (1, 6) and (13, 15)? (a) 225 (b) 16 (c) 21 (d) 15
  25. 25.What is the midpoint of the line joining (0, 1) and (12, 7)? (a) (6, 3) (b) (6, 4) (c) (4, 6) (d) (12, 8)
  26. 26.What is the distance between the points (5, 6) and (21, 18)? (a) 400 (b) 20 (c) 28 (d) 21
  27. 27.What is the midpoint of the line joining (4, 3) and (8, 1)? (a) (2, 6) (b) (12, 4) (c) (2, 1) (d) (6, 2)
  28. 28.What is the distance between the points (8, 6) and (11, 10)? (a) 6 (b) 25 (c) 5 (d) 7
  29. 29.What is the midpoint of the line joining (8, 3) and (14, 7)? (a) (22, 10) (b) (5, 11) (c) (11, 5) (d) (3, 2)
  30. 30.In which quadrant does the point (−5, −5) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  31. 31.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 7 (c) 5 (d) 25
  32. 32.In which quadrant does the point (3, −6) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  33. 33.In which quadrant does the point (−9, −2) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  34. 34.In which quadrant does the point (−9, −7) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  35. 35.What is the midpoint of the line joining (4, 3) and (10, 9)? (a) (14, 12) (b) (6, 7) (c) (3, 3) (d) (7, 6)
  36. 36.What is the distance between the points (9, 24) and (16, 0)? (a) 26 (b) 31 (c) 25 (d) 625
  37. 37.In which quadrant does the point (−4, 4) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  38. 38.In which quadrant does the point (−8, 3) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  39. 39.What is the distance between the points (3, 6) and (11, 12)? (a) 10 (b) 11 (c) 14 (d) 100
  40. 40.In which quadrant does the point (−4, −1) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant

Answer key

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

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