← Coordinates and distance lesson New set →

Coordinate Geometry Worksheet for Maths Olympiad

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

Answer key

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

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