← Coordinates and distance lesson New set →

Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 79 · 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 (9, 1) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  2. 2.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 21 (c) 16 (d) 15
  3. 3.In which quadrant does the point (−1, 3) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  4. 4.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 625 (c) 26 (d) 25
  5. 5.What is the midpoint of the line joining (8, 9) and (16, 3)? (a) (6, 12) (b) (4, 3) (c) (12, 6) (d) (24, 12)
  6. 6.What is the distance between the points (4, 7) and (9, 19)? (a) 169 (b) 13 (c) 17 (d) 14
  7. 7.In which quadrant does the point (8, 1) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  8. 8.What is the distance between the points (3, 4) and (15, 13)? (a) 225 (b) 15 (c) 16 (d) 21
  9. 9.What is the midpoint of the line joining (5, 1) and (17, 9)? (a) (22, 10) (b) (6, 4) (c) (5, 11) (d) (11, 5)
  10. 10.What is the distance between the points (3, 0) and (12, 12)? (a) 21 (b) 16 (c) 225 (d) 15
  11. 11.In which quadrant does the point (−6, −4) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  12. 12.What is the distance between the points (1, 25) and (8, 1)? (a) 625 (b) 31 (c) 26 (d) 25
  13. 13.In which quadrant does the point (−1, 2) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  14. 14.What is the distance between the points (7, 4) and (12, 16)? (a) 17 (b) 14 (c) 13 (d) 169
  15. 15.What is the distance between the points (6, 5) and (21, 13)? (a) 289 (b) 23 (c) 17 (d) 18
  16. 16.In which quadrant does the point (−1, 1) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  17. 17.What is the distance between the points (7, 8) and (31, 1)? (a) 31 (b) 25 (c) 625 (d) 26
  18. 18.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 14 (c) 11 (d) 10
  19. 19.What is the midpoint of the line joining (3, 10) and (11, 6)? (a) (8, 7) (b) (4, 2) (c) (14, 16) (d) (7, 8)
  20. 20.What is the distance between the points (4, 7) and (13, 19)? (a) 21 (b) 225 (c) 15 (d) 16
  21. 21.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 17 (c) 18 (d) 23
  22. 22.In which quadrant does the point (−4, 5) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  23. 23.In which quadrant does the point (−1, −5) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  24. 24.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 169 (c) 13 (d) 17
  25. 25.In which quadrant does the point (−1, −6) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  26. 26.What is the distance between the points (4, 4) and (16, 13)? (a) 225 (b) 21 (c) 16 (d) 15
  27. 27.In which quadrant does the point (7, 6) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  28. 28.What is the distance between the points (9, 8) and (21, 17)? (a) 15 (b) 21 (c) 225 (d) 16
  29. 29.In which quadrant does the point (4, 3) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  30. 30.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 17 (c) 23 (d) 289
  31. 31.How far is the point (24, 7) from the origin (0, 0)? (a) 25 (b) 31 (c) 625 (d) 26
  32. 32.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 100 (c) 11 (d) 14
  33. 33.What is the distance between the points (3, 3) and (10, 27)? (a) 31 (b) 25 (c) 625 (d) 26
  34. 34.What is the distance between the points (4, 8) and (28, 1)? (a) 625 (b) 31 (c) 26 (d) 25
  35. 35.What is the distance between the points (3, 2) and (15, 11)? (a) 16 (b) 15 (c) 225 (d) 21
  36. 36.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 6 (c) 5 (d) 25
  37. 37.What is the distance between the points (0, 5) and (24, 12)? (a) 625 (b) 31 (c) 26 (d) 25
  38. 38.What is the midpoint of the line joining (10, 6) and (12, 12)? (a) (1, 3) (b) (22, 18) (c) (11, 9) (d) (9, 11)
  39. 39.What is the distance between the points (8, 8) and (14, 0)? (a) 10 (b) 100 (c) 14 (d) 11
  40. 40.What is the midpoint of the line joining (10, 6) and (18, 12)? (a) (4, 3) (b) (28, 18) (c) (9, 14) (d) (14, 9)

Answer key

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

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