← Coordinates and distance lesson New set →

Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 974 · 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, 4) and (16, 20)? (a) 21 (b) 28 (c) 20 (d) 400
  2. 2.What is the midpoint of the line joining (0, 1) and (4, 13)? (a) (4, 14) (b) (2, 6) (c) (2, 7) (d) (7, 2)
  3. 3.What is the distance between the points (2, 8) and (6, 5)? (a) 7 (b) 6 (c) 5 (d) 25
  4. 4.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 7 (c) 6 (d) 5
  5. 5.What is the midpoint of the line joining (7, 3) and (9, 11)? (a) (16, 14) (b) (7, 8) (c) (8, 7) (d) (1, 4)
  6. 6.What is the distance between the points (3, 21) and (15, 5)? (a) 28 (b) 400 (c) 20 (d) 21
  7. 7.In which quadrant does the point (7, 7) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  8. 8.In which quadrant does the point (−2, 1) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  9. 9.What is the distance between the points (5, 23) and (13, 8)? (a) 289 (b) 18 (c) 17 (d) 23
  10. 10.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 23 (c) 17 (d) 18
  11. 11.What is the distance between the points (1, 13) and (13, 4)? (a) 16 (b) 21 (c) 15 (d) 225
  12. 12.What is the distance between the points (7, 3) and (10, 7)? (a) 7 (b) 25 (c) 6 (d) 5
  13. 13.What is the distance between the points (0, 16) and (9, 4)? (a) 15 (b) 21 (c) 16 (d) 225
  14. 14.In which quadrant does the point (3, 5) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  15. 15.What is the midpoint of the line joining (2, 4) and (12, 6)? (a) (5, 7) (b) (14, 10) (c) (7, 5) (d) (5, 1)
  16. 16.What is the midpoint of the line joining (6, 5) and (10, 7)? (a) (16, 12) (b) (6, 8) (c) (2, 1) (d) (8, 6)
  17. 17.What is the distance between the points (8, 12) and (20, 3)? (a) 225 (b) 15 (c) 21 (d) 16
  18. 18.What is the distance between the points (1, 2) and (5, 5)? (a) 7 (b) 6 (c) 5 (d) 25
  19. 19.What is the midpoint of the line joining (1, 2) and (3, 0)? (a) (1, 1) (b) (4, 2) (c) (1, 2) (d) (2, 1)
  20. 20.What is the distance between the points (8, 0) and (17, 12)? (a) 15 (b) 21 (c) 225 (d) 16
  21. 21.How far is the point (12, 9) from the origin (0, 0)? (a) 16 (b) 225 (c) 21 (d) 15
  22. 22.What is the midpoint of the line joining (4, 10) and (14, 16)? (a) (5, 3) (b) (13, 9) (c) (9, 13) (d) (18, 26)
  23. 23.What is the distance between the points (0, 0) and (4, 3)? (a) 5 (b) 7 (c) 25 (d) 6
  24. 24.What is the distance between the points (3, 4) and (6, 8)? (a) 6 (b) 5 (c) 7 (d) 25
  25. 25.What is the midpoint of the line joining (0, 5) and (2, 1)? (a) (2, 6) (b) (1, 3) (c) (1, 2) (d) (3, 1)
  26. 26.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 100 (c) 14 (d) 10
  27. 27.What is the midpoint of the line joining (1, 7) and (9, 1)? (a) (10, 8) (b) (5, 4) (c) (4, 5) (d) (4, 3)
  28. 28.What is the midpoint of the line joining (5, 7) and (9, 1)? (a) (7, 4) (b) (14, 8) (c) (4, 7) (d) (2, 3)
  29. 29.What is the midpoint of the line joining (1, 3) and (9, 11)? (a) (7, 5) (b) (5, 7) (c) (10, 14) (d) (4, 4)
  30. 30.What is the midpoint of the line joining (4, 10) and (10, 4)? (a) (7, 7) (b) (14, 14) (c) (8, 7) (d) (3, 3)
  31. 31.What is the midpoint of the line joining (6, 2) and (14, 0)? (a) (1, 10) (b) (10, 1) (c) (20, 2) (d) (4, 1)
  32. 32.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 28 (c) 21 (d) 400
  33. 33.In which quadrant does the point (9, −5) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  34. 34.What is the distance between the points (0, 3) and (4, 0)? (a) 25 (b) 7 (c) 6 (d) 5
  35. 35.In which quadrant does the point (4, −8) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  36. 36.In which quadrant does the point (−2, 2) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  37. 37.In which quadrant does the point (2, −1) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  38. 38.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 14 (c) 13 (d) 169
  39. 39.In which quadrant does the point (−3, 5) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  40. 40.What is the distance between the points (7, 6) and (12, 18)? (a) 169 (b) 14 (c) 17 (d) 13

Answer key

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

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