← Coordinates and distance lesson New set →

Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 209 · 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 (3, 3) and (6, 7)? (a) 7 (b) 5 (c) 25 (d) 6
  2. 2.What is the distance between the points (8, 2) and (15, 26)? (a) 31 (b) 625 (c) 26 (d) 25
  3. 3.What is the midpoint of the line joining (1, 3) and (11, 15)? (a) (5, 6) (b) (6, 9) (c) (12, 18) (d) (9, 6)
  4. 4.What is the midpoint of the line joining (7, 2) and (11, 8)? (a) (18, 10) (b) (2, 3) (c) (5, 9) (d) (9, 5)
  5. 5.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 21 (c) 20 (d) 400
  6. 6.What is the distance between the points (3, 8) and (15, 24)? (a) 20 (b) 28 (c) 21 (d) 400
  7. 7.What is the midpoint of the line joining (8, 19) and (20, 9)? (a) (15, 14) (b) (6, 5) (c) (28, 28) (d) (14, 14)
  8. 8.What is the distance between the points (5, 9) and (21, 21)? (a) 28 (b) 400 (c) 21 (d) 20
  9. 9.In which quadrant does the point (−2, 8) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  10. 10.What is the distance between the points (1, 29) and (8, 5)? (a) 31 (b) 26 (c) 625 (d) 25
  11. 11.What is the midpoint of the line joining (9, 2) and (13, 8)? (a) (11, 5) (b) (2, 3) (c) (22, 10) (d) (5, 11)
  12. 12.What is the distance between the points (7, 13) and (19, 4)? (a) 16 (b) 225 (c) 15 (d) 21
  13. 13.What is the midpoint of the line joining (6, 17) and (16, 7)? (a) (22, 24) (b) (5, 5) (c) (11, 12) (d) (12, 11)
  14. 14.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 169 (c) 14 (d) 13
  15. 15.What is the distance between the points (0, 3) and (3, 7)? (a) 7 (b) 6 (c) 5 (d) 25
  16. 16.What is the distance between the points (2, 2) and (14, 7)? (a) 169 (b) 17 (c) 14 (d) 13
  17. 17.What is the distance between the points (4, 24) and (11, 0)? (a) 31 (b) 625 (c) 25 (d) 26
  18. 18.In which quadrant does the point (−8, 1) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  19. 19.In which quadrant does the point (−4, 3) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  20. 20.What is the distance between the points (8, 4) and (20, 13)? (a) 15 (b) 16 (c) 21 (d) 225
  21. 21.In which quadrant does the point (5, −1) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  22. 22.What is the distance between the points (8, 8) and (23, 0)? (a) 289 (b) 23 (c) 17 (d) 18
  23. 23.What is the midpoint of the line joining (5, 13) and (13, 5)? (a) (10, 9) (b) (18, 18) (c) (9, 9) (d) (4, 4)
  24. 24.What is the midpoint of the line joining (5, 10) and (17, 2)? (a) (11, 6) (b) (6, 4) (c) (22, 12) (d) (6, 11)
  25. 25.What is the distance between the points (1, 11) and (5, 8)? (a) 25 (b) 5 (c) 7 (d) 6
  26. 26.How far is the point (4, 3) from the origin (0, 0)? (a) 5 (b) 25 (c) 7 (d) 6
  27. 27.What is the distance between the points (4, 18) and (13, 6)? (a) 16 (b) 21 (c) 15 (d) 225
  28. 28.What is the distance between the points (4, 5) and (13, 17)? (a) 16 (b) 21 (c) 225 (d) 15
  29. 29.What is the midpoint of the line joining (1, 12) and (5, 6)? (a) (3, 9) (b) (2, 3) (c) (9, 3) (d) (6, 18)
  30. 30.What is the distance between the points (2, 9) and (14, 14)? (a) 13 (b) 17 (c) 14 (d) 169
  31. 31.What is the distance between the points (0, 7) and (3, 11)? (a) 25 (b) 5 (c) 7 (d) 6
  32. 32.What is the midpoint of the line joining (7, 2) and (19, 14)? (a) (26, 16) (b) (13, 8) (c) (8, 13) (d) (6, 6)
  33. 33.What is the midpoint of the line joining (10, 8) and (22, 6)? (a) (7, 16) (b) (32, 14) (c) (6, 1) (d) (16, 7)
  34. 34.What is the midpoint of the line joining (1, 12) and (13, 0)? (a) (6, 7) (b) (6, 6) (c) (7, 6) (d) (14, 12)
  35. 35.What is the distance between the points (4, 20) and (9, 8)? (a) 13 (b) 14 (c) 169 (d) 17
  36. 36.What is the midpoint of the line joining (3, 4) and (13, 2)? (a) (16, 6) (b) (3, 8) (c) (8, 3) (d) (5, 1)
  37. 37.In which quadrant does the point (−9, 3) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  38. 38.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 6 (c) 5 (d) 7
  39. 39.What is the midpoint of the line joining (6, 1) and (12, 5)? (a) (3, 2) (b) (3, 9) (c) (18, 6) (d) (9, 3)
  40. 40.In which quadrant does the point (−9, −5) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant

Answer key

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

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