← Coordinates and distance lesson New set →

Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 405 · 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, 2) and (12, 7)? (a) 17 (b) 169 (c) 13 (d) 14
  2. 2.What is the midpoint of the line joining (1, 7) and (3, 15)? (a) (11, 2) (b) (1, 4) (c) (2, 11) (d) (4, 22)
  3. 3.In which quadrant does the point (9, 5) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  4. 4.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 400 (c) 28 (d) 20
  5. 5.What is the distance between the points (8, 2) and (16, 17)? (a) 18 (b) 17 (c) 289 (d) 23
  6. 6.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 289 (c) 17 (d) 23
  7. 7.What is the distance between the points (1, 14) and (9, 8)? (a) 11 (b) 14 (c) 10 (d) 100
  8. 8.What is the distance between the points (4, 7) and (8, 10)? (a) 25 (b) 5 (c) 7 (d) 6
  9. 9.What is the distance between the points (0, 2) and (16, 14)? (a) 21 (b) 28 (c) 20 (d) 400
  10. 10.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 7 (c) 6 (d) 5
  11. 11.In which quadrant does the point (−8, −1) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  12. 12.What is the distance between the points (2, 16) and (10, 1)? (a) 23 (b) 289 (c) 18 (d) 17
  13. 13.What is the midpoint of the line joining (5, 7) and (11, 11)? (a) (8, 9) (b) (9, 8) (c) (16, 18) (d) (3, 2)
  14. 14.In which quadrant does the point (9, 8) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  15. 15.In which quadrant does the point (−5, −5) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  16. 16.What is the midpoint of the line joining (7, 0) and (17, 2)? (a) (24, 2) (b) (12, 1) (c) (1, 12) (d) (5, 1)
  17. 17.What is the midpoint of the line joining (8, 18) and (20, 10)? (a) (15, 14) (b) (6, 4) (c) (28, 28) (d) (14, 14)
  18. 18.What is the midpoint of the line joining (0, 15) and (10, 5)? (a) (5, 5) (b) (10, 20) (c) (10, 5) (d) (5, 10)
  19. 19.In which quadrant does the point (−3, −1) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  20. 20.What is the distance between the points (2, 9) and (10, 24)? (a) 23 (b) 18 (c) 17 (d) 289
  21. 21.What is the distance between the points (0, 2) and (8, 17)? (a) 23 (b) 18 (c) 289 (d) 17
  22. 22.What is the distance between the points (3, 4) and (11, 19)? (a) 18 (b) 23 (c) 17 (d) 289
  23. 23.What is the midpoint of the line joining (3, 2) and (15, 0)? (a) (18, 2) (b) (1, 9) (c) (9, 1) (d) (6, 1)
  24. 24.In which quadrant does the point (7, 6) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  25. 25.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 11 (c) 100 (d) 10
  26. 26.What is the midpoint of the line joining (0, 4) and (10, 2)? (a) (3, 5) (b) (5, 3) (c) (10, 6) (d) (5, 1)
  27. 27.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 26 (c) 625 (d) 25
  28. 28.What is the distance between the points (4, 11) and (7, 7)? (a) 7 (b) 6 (c) 25 (d) 5
  29. 29.What is the distance between the points (0, 18) and (8, 3)? (a) 17 (b) 18 (c) 23 (d) 289
  30. 30.How far is the point (4, 3) from the origin (0, 0)? (a) 5 (b) 7 (c) 6 (d) 25
  31. 31.What is the distance between the points (9, 9) and (21, 18)? (a) 15 (b) 21 (c) 16 (d) 225
  32. 32.What is the distance between the points (5, 13) and (13, 7)? (a) 100 (b) 14 (c) 11 (d) 10
  33. 33.In which quadrant does the point (9, 9) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  34. 34.What is the distance between the points (3, 16) and (15, 0)? (a) 21 (b) 28 (c) 400 (d) 20
  35. 35.In which quadrant does the point (1, −1) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  36. 36.What is the distance between the points (1, 1) and (8, 25)? (a) 25 (b) 625 (c) 26 (d) 31
  37. 37.What is the distance between the points (3, 6) and (9, 14)? (a) 10 (b) 11 (c) 100 (d) 14
  38. 38.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 11 (c) 10 (d) 100
  39. 39.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 15 (c) 21 (d) 225
  40. 40.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 14 (c) 13 (d) 17

Answer key

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

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