← Coordinates and distance lesson New set →

Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 226 · 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 (6, 8) and (14, 23)? (a) 23 (b) 289 (c) 17 (d) 18
  2. 2.What is the midpoint of the line joining (5, 14) and (13, 6)? (a) (10, 9) (b) (18, 20) (c) (9, 10) (d) (4, 4)
  3. 3.In which quadrant does the point (6, −7) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  4. 4.In which quadrant does the point (−4, 5) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  5. 5.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 21 (c) 20 (d) 400
  6. 6.What is the midpoint of the line joining (3, 3) and (13, 15)? (a) (16, 18) (b) (8, 9) (c) (5, 6) (d) (9, 8)
  7. 7.What is the distance between the points (4, 6) and (28, 13)? (a) 25 (b) 26 (c) 31 (d) 625
  8. 8.What is the midpoint of the line joining (4, 11) and (16, 9)? (a) (6, 1) (b) (20, 20) (c) (10, 10) (d) (11, 10)
  9. 9.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 15 (c) 21 (d) 16
  10. 10.What is the midpoint of the line joining (0, 4) and (8, 8)? (a) (4, 2) (b) (4, 6) (c) (6, 4) (d) (8, 12)
  11. 11.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 25 (c) 31 (d) 26
  12. 12.What is the midpoint of the line joining (1, 5) and (3, 1)? (a) (1, 2) (b) (2, 3) (c) (3, 2) (d) (4, 6)
  13. 13.In which quadrant does the point (−1, 5) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  14. 14.What is the midpoint of the line joining (7, 18) and (19, 10)? (a) (26, 28) (b) (14, 13) (c) (13, 14) (d) (6, 4)
  15. 15.What is the distance between the points (1, 1) and (13, 17)? (a) 20 (b) 400 (c) 21 (d) 28
  16. 16.In which quadrant does the point (−6, −7) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  17. 17.In which quadrant does the point (2, 6) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  18. 18.In which quadrant does the point (−2, 2) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  19. 19.What is the midpoint of the line joining (3, 14) and (7, 8)? (a) (5, 11) (b) (2, 3) (c) (11, 5) (d) (10, 22)
  20. 20.What is the midpoint of the line joining (9, 4) and (13, 16)? (a) (2, 6) (b) (11, 10) (c) (10, 11) (d) (22, 20)
  21. 21.What is the midpoint of the line joining (6, 6) and (14, 2)? (a) (4, 2) (b) (4, 10) (c) (20, 8) (d) (10, 4)
  22. 22.What is the distance between the points (9, 21) and (25, 9)? (a) 20 (b) 28 (c) 21 (d) 400
  23. 23.In which quadrant does the point (6, 5) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  24. 24.What is the midpoint of the line joining (9, 10) and (19, 20)? (a) (15, 14) (b) (14, 15) (c) (28, 30) (d) (5, 5)
  25. 25.What is the distance between the points (3, 10) and (9, 2)? (a) 14 (b) 100 (c) 10 (d) 11
  26. 26.What is the midpoint of the line joining (0, 12) and (10, 6)? (a) (10, 18) (b) (5, 3) (c) (5, 9) (d) (9, 5)
  27. 27.In which quadrant does the point (1, 9) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  28. 28.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 17 (c) 289 (d) 18
  29. 29.What is the distance between the points (5, 20) and (13, 5)? (a) 23 (b) 289 (c) 18 (d) 17
  30. 30.In which quadrant does the point (−6, −2) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  31. 31.What is the midpoint of the line joining (10, 7) and (20, 5)? (a) (5, 1) (b) (30, 12) (c) (6, 15) (d) (15, 6)
  32. 32.What is the midpoint of the line joining (3, 6) and (9, 0)? (a) (3, 3) (b) (6, 3) (c) (12, 6) (d) (3, 6)
  33. 33.What is the midpoint of the line joining (8, 15) and (12, 3)? (a) (20, 18) (b) (2, 6) (c) (10, 9) (d) (9, 10)
  34. 34.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 7 (c) 6 (d) 5
  35. 35.What is the distance between the points (4, 18) and (12, 3)? (a) 23 (b) 17 (c) 289 (d) 18
  36. 36.In which quadrant does the point (8, −9) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  37. 37.In which quadrant does the point (−8, 6) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  38. 38.What is the distance between the points (4, 16) and (16, 7)? (a) 225 (b) 21 (c) 16 (d) 15
  39. 39.In which quadrant does the point (7, −3) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  40. 40.In which quadrant does the point (9, 3) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant

Answer key

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

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