← Coordinates and distance lesson New set →

Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 66 · 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 (0, 8) and (6, 16)? (a) 14 (b) 100 (c) 11 (d) 10
  2. 2.What is the midpoint of the line joining (6, 9) and (8, 17)? (a) (13, 7) (b) (1, 4) (c) (14, 26) (d) (7, 13)
  3. 3.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 5 (c) 25 (d) 7
  4. 4.In which quadrant does the point (−3, 6) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  5. 5.What is the distance between the points (3, 8) and (18, 0)? (a) 18 (b) 289 (c) 23 (d) 17
  6. 6.What is the midpoint of the line joining (0, 5) and (4, 3)? (a) (4, 8) (b) (2, 1) (c) (2, 4) (d) (4, 2)
  7. 7.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 15 (c) 225 (d) 21
  8. 8.What is the distance between the points (3, 18) and (19, 6)? (a) 21 (b) 400 (c) 28 (d) 20
  9. 9.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 17 (c) 289 (d) 18
  10. 10.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 289 (c) 17 (d) 18
  11. 11.In which quadrant does the point (−2, 1) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  12. 12.In which quadrant does the point (−7, −2) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  13. 13.In which quadrant does the point (7, −7) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  14. 14.How far is the point (12, 16) from the origin (0, 0)? (a) 20 (b) 21 (c) 400 (d) 28
  15. 15.In which quadrant does the point (−2, 9) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  16. 16.What is the distance between the points (1, 7) and (4, 3)? (a) 7 (b) 6 (c) 5 (d) 25
  17. 17.What is the distance between the points (8, 22) and (20, 6)? (a) 20 (b) 21 (c) 400 (d) 28
  18. 18.In which quadrant does the point (6, 7) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  19. 19.What is the midpoint of the line joining (8, 6) and (16, 4)? (a) (5, 12) (b) (4, 1) (c) (12, 5) (d) (24, 10)
  20. 20.What is the midpoint of the line joining (0, 4) and (12, 16)? (a) (6, 10) (b) (12, 20) (c) (6, 6) (d) (10, 6)
  21. 21.What is the distance between the points (6, 6) and (14, 21)? (a) 23 (b) 18 (c) 289 (d) 17
  22. 22.What is the distance between the points (1, 10) and (9, 4)? (a) 11 (b) 10 (c) 100 (d) 14
  23. 23.What is the distance between the points (9, 12) and (13, 9)? (a) 5 (b) 6 (c) 7 (d) 25
  24. 24.What is the midpoint of the line joining (7, 0) and (17, 8)? (a) (4, 12) (b) (12, 4) (c) (5, 4) (d) (24, 8)
  25. 25.What is the midpoint of the line joining (1, 4) and (3, 10)? (a) (4, 14) (b) (7, 2) (c) (2, 7) (d) (1, 3)
  26. 26.What is the distance between the points (0, 8) and (12, 24)? (a) 28 (b) 21 (c) 400 (d) 20
  27. 27.What is the distance between the points (8, 19) and (24, 7)? (a) 400 (b) 28 (c) 21 (d) 20
  28. 28.How far is the point (24, 7) from the origin (0, 0)? (a) 26 (b) 31 (c) 25 (d) 625
  29. 29.In which quadrant does the point (−1, −9) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  30. 30.What is the midpoint of the line joining (3, 1) and (7, 7)? (a) (5, 4) (b) (2, 3) (c) (4, 5) (d) (10, 8)
  31. 31.What is the distance between the points (9, 1) and (21, 17)? (a) 28 (b) 21 (c) 20 (d) 400
  32. 32.In which quadrant does the point (−1, 3) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  33. 33.What is the distance between the points (4, 1) and (16, 6)? (a) 17 (b) 169 (c) 14 (d) 13
  34. 34.What is the distance between the points (1, 3) and (13, 8)? (a) 17 (b) 13 (c) 169 (d) 14
  35. 35.What is the midpoint of the line joining (7, 7) and (15, 13)? (a) (22, 20) (b) (11, 10) (c) (4, 3) (d) (10, 11)
  36. 36.What is the midpoint of the line joining (3, 1) and (15, 9)? (a) (5, 9) (b) (9, 5) (c) (6, 4) (d) (18, 10)
  37. 37.What is the distance between the points (6, 6) and (11, 18)? (a) 169 (b) 17 (c) 14 (d) 13
  38. 38.In which quadrant does the point (−7, 4) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  39. 39.In which quadrant does the point (9, 2) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  40. 40.What is the midpoint of the line joining (2, 10) and (12, 0)? (a) (14, 10) (b) (7, 5) (c) (5, 7) (d) (5, 5)

Answer key

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

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