← Coordinates and distance lesson New set →

Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 151 · 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.In which quadrant does the point (3, −7) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  2. 2.What is the midpoint of the line joining (0, 4) and (10, 8)? (a) (6, 5) (b) (5, 2) (c) (10, 12) (d) (5, 6)
  3. 3.In which quadrant does the point (2, 4) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  4. 4.What is the midpoint of the line joining (0, 11) and (10, 3)? (a) (5, 7) (b) (7, 5) (c) (5, 4) (d) (10, 14)
  5. 5.What is the distance between the points (2, 4) and (9, 28)? (a) 25 (b) 31 (c) 26 (d) 625
  6. 6.What is the distance between the points (3, 7) and (19, 19)? (a) 400 (b) 20 (c) 21 (d) 28
  7. 7.How far is the point (12, 9) from the origin (0, 0)? (a) 16 (b) 225 (c) 15 (d) 21
  8. 8.In which quadrant does the point (7, −7) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  9. 9.What is the distance between the points (1, 24) and (9, 9)? (a) 18 (b) 289 (c) 23 (d) 17
  10. 10.In which quadrant does the point (−2, −2) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  11. 11.In which quadrant does the point (1, −4) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  12. 12.In which quadrant does the point (4, 9) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  13. 13.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 21 (c) 20 (d) 28
  14. 14.What is the distance between the points (0, 9) and (7, 33)? (a) 625 (b) 26 (c) 31 (d) 25
  15. 15.What is the distance between the points (2, 9) and (14, 14)? (a) 17 (b) 169 (c) 14 (d) 13
  16. 16.What is the midpoint of the line joining (4, 10) and (16, 8)? (a) (6, 1) (b) (9, 10) (c) (20, 18) (d) (10, 9)
  17. 17.In which quadrant does the point (1, −1) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  18. 18.In which quadrant does the point (−9, −3) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  19. 19.What is the midpoint of the line joining (3, 8) and (15, 14)? (a) (11, 9) (b) (9, 11) (c) (6, 3) (d) (18, 22)
  20. 20.What is the midpoint of the line joining (9, 9) and (11, 21)? (a) (1, 6) (b) (20, 30) (c) (10, 15) (d) (15, 10)
  21. 21.What is the midpoint of the line joining (8, 9) and (16, 5)? (a) (7, 12) (b) (12, 7) (c) (24, 14) (d) (4, 2)
  22. 22.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 400 (c) 20 (d) 28
  23. 23.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 6 (c) 5 (d) 7
  24. 24.What is the distance between the points (8, 6) and (13, 18)? (a) 169 (b) 13 (c) 17 (d) 14
  25. 25.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 11 (c) 10 (d) 14
  26. 26.What is the midpoint of the line joining (1, 2) and (13, 4)? (a) (14, 6) (b) (7, 3) (c) (6, 1) (d) (3, 7)
  27. 27.What is the midpoint of the line joining (3, 11) and (5, 5)? (a) (1, 3) (b) (4, 8) (c) (8, 16) (d) (8, 4)
  28. 28.What is the distance between the points (7, 7) and (15, 22)? (a) 289 (b) 18 (c) 17 (d) 23
  29. 29.In which quadrant does the point (8, 6) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  30. 30.What is the distance between the points (4, 20) and (13, 8)? (a) 16 (b) 225 (c) 21 (d) 15
  31. 31.What is the midpoint of the line joining (7, 13) and (11, 9)? (a) (2, 2) (b) (18, 22) (c) (11, 9) (d) (9, 11)
  32. 32.In which quadrant does the point (3, 2) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  33. 33.What is the midpoint of the line joining (1, 16) and (9, 8)? (a) (12, 5) (b) (10, 24) (c) (5, 12) (d) (4, 4)
  34. 34.What is the distance between the points (5, 12) and (9, 9)? (a) 25 (b) 7 (c) 6 (d) 5
  35. 35.What is the midpoint of the line joining (5, 2) and (17, 14)? (a) (8, 11) (b) (22, 16) (c) (11, 8) (d) (6, 6)
  36. 36.What is the distance between the points (7, 16) and (19, 7)? (a) 21 (b) 225 (c) 16 (d) 15
  37. 37.What is the midpoint of the line joining (9, 4) and (13, 2)? (a) (11, 3) (b) (22, 6) (c) (3, 11) (d) (2, 1)
  38. 38.What is the distance between the points (0, 13) and (24, 6)? (a) 26 (b) 625 (c) 25 (d) 31
  39. 39.What is the distance between the points (9, 6) and (21, 1)? (a) 17 (b) 169 (c) 13 (d) 14
  40. 40.How far is the point (24, 7) from the origin (0, 0)? (a) 26 (b) 31 (c) 25 (d) 625

Answer key

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

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