← Coordinates and distance lesson New set →

Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 664 · 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.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 169 (c) 13 (d) 14
  2. 2.What is the midpoint of the line joining (9, 8) and (17, 6)? (a) (26, 14) (b) (7, 13) (c) (13, 7) (d) (4, 1)
  3. 3.In which quadrant does the point (−5, 3) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  4. 4.What is the midpoint of the line joining (2, 7) and (14, 9)? (a) (8, 8) (b) (6, 1) (c) (9, 8) (d) (16, 16)
  5. 5.What is the distance between the points (8, 5) and (20, 21)? (a) 28 (b) 400 (c) 20 (d) 21
  6. 6.In which quadrant does the point (2, 7) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  7. 7.What is the distance between the points (2, 4) and (7, 16)? (a) 14 (b) 13 (c) 17 (d) 169
  8. 8.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 14 (c) 100 (d) 10
  9. 9.What is the midpoint of the line joining (7, 10) and (11, 14)? (a) (12, 9) (b) (9, 12) (c) (2, 2) (d) (18, 24)
  10. 10.In which quadrant does the point (5, −4) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  11. 11.In which quadrant does the point (−1, 9) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  12. 12.What is the midpoint of the line joining (8, 1) and (16, 5)? (a) (3, 12) (b) (24, 6) (c) (4, 2) (d) (12, 3)
  13. 13.What is the distance between the points (9, 9) and (33, 16)? (a) 25 (b) 625 (c) 26 (d) 31
  14. 14.In which quadrant does the point (−8, 8) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  15. 15.What is the distance between the points (7, 3) and (14, 27)? (a) 31 (b) 25 (c) 625 (d) 26
  16. 16.In which quadrant does the point (−1, 4) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  17. 17.What is the midpoint of the line joining (9, 1) and (11, 11)? (a) (1, 5) (b) (6, 10) (c) (10, 6) (d) (20, 12)
  18. 18.How far is the point (15, 8) from the origin (0, 0)? (a) 17 (b) 18 (c) 289 (d) 23
  19. 19.What is the distance between the points (4, 9) and (19, 1)? (a) 18 (b) 289 (c) 23 (d) 17
  20. 20.What is the midpoint of the line joining (0, 6) and (10, 16)? (a) (5, 11) (b) (10, 22) (c) (5, 5) (d) (11, 5)
  21. 21.What is the midpoint of the line joining (2, 4) and (4, 0)? (a) (1, 2) (b) (2, 3) (c) (3, 2) (d) (6, 4)
  22. 22.What is the midpoint of the line joining (1, 8) and (5, 20)? (a) (6, 28) (b) (14, 3) (c) (2, 6) (d) (3, 14)
  23. 23.In which quadrant does the point (6, −3) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  24. 24.What is the distance between the points (6, 7) and (30, 0)? (a) 31 (b) 25 (c) 625 (d) 26
  25. 25.What is the distance between the points (8, 3) and (13, 15)? (a) 169 (b) 17 (c) 14 (d) 13
  26. 26.What is the distance between the points (5, 0) and (17, 16)? (a) 28 (b) 400 (c) 20 (d) 21
  27. 27.In which quadrant does the point (9, −8) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  28. 28.What is the distance between the points (2, 4) and (11, 16)? (a) 225 (b) 21 (c) 15 (d) 16
  29. 29.What is the distance between the points (5, 9) and (13, 15)? (a) 10 (b) 100 (c) 14 (d) 11
  30. 30.What is the distance between the points (5, 4) and (17, 9)? (a) 14 (b) 169 (c) 13 (d) 17
  31. 31.What is the distance between the points (2, 21) and (10, 6)? (a) 17 (b) 18 (c) 23 (d) 289
  32. 32.In which quadrant does the point (−4, 4) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  33. 33.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 25 (c) 5 (d) 7
  34. 34.What is the distance between the points (9, 17) and (18, 5)? (a) 15 (b) 225 (c) 16 (d) 21
  35. 35.What is the distance between the points (5, 6) and (12, 30)? (a) 31 (b) 26 (c) 25 (d) 625
  36. 36.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 5 (c) 6 (d) 7
  37. 37.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 400 (c) 20 (d) 28
  38. 38.What is the midpoint of the line joining (8, 3) and (16, 1)? (a) (4, 1) (b) (2, 12) (c) (24, 4) (d) (12, 2)
  39. 39.What is the midpoint of the line joining (6, 17) and (16, 5)? (a) (5, 6) (b) (12, 11) (c) (22, 22) (d) (11, 11)
  40. 40.In which quadrant does the point (−6, −5) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant

Answer key

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

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