← Coordinates and distance lesson New set →

Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 860 · 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 (5, 12) and (20, 4)? (a) 18 (b) 17 (c) 289 (d) 23
  2. 2.What is the midpoint of the line joining (10, 16) and (20, 6)? (a) (30, 22) (b) (15, 11) (c) (11, 15) (d) (5, 5)
  3. 3.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 21 (c) 20 (d) 400
  4. 4.In which quadrant does the point (−1, 5) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  5. 5.In which quadrant does the point (5, −1) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  6. 6.What is the distance between the points (9, 11) and (33, 4)? (a) 625 (b) 31 (c) 25 (d) 26
  7. 7.What is the midpoint of the line joining (1, 17) and (7, 5)? (a) (4, 11) (b) (11, 4) (c) (3, 6) (d) (8, 22)
  8. 8.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 289 (c) 23 (d) 18
  9. 9.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 5 (c) 7 (d) 6
  10. 10.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 100 (c) 11 (d) 10
  11. 11.What is the distance between the points (7, 16) and (16, 4)? (a) 21 (b) 16 (c) 15 (d) 225
  12. 12.What is the distance between the points (3, 16) and (15, 7)? (a) 15 (b) 16 (c) 225 (d) 21
  13. 13.In which quadrant does the point (−5, 2) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  14. 14.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 169 (c) 14 (d) 13
  15. 15.In which quadrant does the point (2, 8) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  16. 16.What is the distance between the points (8, 9) and (12, 12)? (a) 5 (b) 25 (c) 6 (d) 7
  17. 17.In which quadrant does the point (−6, 7) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  18. 18.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 7 (c) 6 (d) 25
  19. 19.What is the distance between the points (2, 5) and (6, 8)? (a) 7 (b) 25 (c) 5 (d) 6
  20. 20.What is the distance between the points (7, 1) and (31, 8)? (a) 625 (b) 31 (c) 26 (d) 25
  21. 21.What is the distance between the points (2, 2) and (10, 17)? (a) 23 (b) 18 (c) 17 (d) 289
  22. 22.What is the distance between the points (3, 7) and (15, 23)? (a) 28 (b) 21 (c) 20 (d) 400
  23. 23.What is the distance between the points (0, 0) and (6, 8)? (a) 14 (b) 11 (c) 10 (d) 100
  24. 24.In which quadrant does the point (4, 7) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  25. 25.In which quadrant does the point (8, 8) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  26. 26.In which quadrant does the point (1, −4) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  27. 27.What is the midpoint of the line joining (6, 0) and (8, 6)? (a) (7, 3) (b) (1, 3) (c) (14, 6) (d) (3, 7)
  28. 28.How far is the point (16, 12) from the origin (0, 0)? (a) 400 (b) 20 (c) 28 (d) 21
  29. 29.What is the distance between the points (4, 15) and (16, 6)? (a) 16 (b) 225 (c) 21 (d) 15
  30. 30.In which quadrant does the point (−4, 2) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  31. 31.In which quadrant does the point (−6, −2) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  32. 32.What is the distance between the points (2, 6) and (10, 12)? (a) 11 (b) 14 (c) 10 (d) 100
  33. 33.What is the midpoint of the line joining (5, 3) and (13, 5)? (a) (4, 1) (b) (9, 4) (c) (18, 8) (d) (4, 9)
  34. 34.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 10 (c) 100 (d) 11
  35. 35.How far is the point (9, 12) from the origin (0, 0)? (a) 15 (b) 21 (c) 225 (d) 16
  36. 36.In which quadrant does the point (−1, −9) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  37. 37.What is the midpoint of the line joining (8, 10) and (14, 18)? (a) (11, 14) (b) (14, 11) (c) (3, 4) (d) (22, 28)
  38. 38.What is the distance between the points (0, 5) and (6, 13)? (a) 14 (b) 100 (c) 10 (d) 11
  39. 39.In which quadrant does the point (−5, −7) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  40. 40.In which quadrant does the point (2, 3) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant

Answer key

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

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