← Coordinates and distance lesson New set →

Coordinate Geometry Worksheet for Maths Olympiad

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

Answer key

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

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