← Coordinates and distance lesson New set →

Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 71 · 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 (1, 10) and (25, 3)? (a) 26 (b) 31 (c) 25 (d) 625
  2. 2.What is the distance between the points (2, 18) and (14, 9)? (a) 21 (b) 15 (c) 225 (d) 16
  3. 3.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 6 (c) 7 (d) 5
  4. 4.How far is the point (12, 9) from the origin (0, 0)? (a) 16 (b) 225 (c) 21 (d) 15
  5. 5.What is the midpoint of the line joining (1, 10) and (11, 14)? (a) (12, 24) (b) (12, 6) (c) (5, 2) (d) (6, 12)
  6. 6.What is the distance between the points (8, 9) and (12, 12)? (a) 5 (b) 7 (c) 6 (d) 25
  7. 7.What is the distance between the points (8, 12) and (23, 4)? (a) 23 (b) 17 (c) 289 (d) 18
  8. 8.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 26 (c) 31 (d) 25
  9. 9.What is the midpoint of the line joining (0, 0) and (8, 8)? (a) (5, 4) (b) (4, 5) (c) (4, 4) (d) (8, 8)
  10. 10.In which quadrant does the point (1, 6) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  11. 11.In which quadrant does the point (−4, −9) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  12. 12.What is the distance between the points (7, 6) and (15, 12)? (a) 100 (b) 10 (c) 11 (d) 14
  13. 13.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 10 (c) 11 (d) 100
  14. 14.What is the midpoint of the line joining (2, 6) and (8, 2)? (a) (4, 5) (b) (5, 4) (c) (3, 2) (d) (10, 8)
  15. 15.What is the distance between the points (1, 1) and (4, 5)? (a) 7 (b) 6 (c) 5 (d) 25
  16. 16.In which quadrant does the point (−5, −1) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  17. 17.What is the distance between the points (2, 14) and (26, 7)? (a) 625 (b) 26 (c) 31 (d) 25
  18. 18.In which quadrant does the point (−1, −2) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  19. 19.In which quadrant does the point (2, 6) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  20. 20.In which quadrant does the point (−5, 5) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  21. 21.What is the midpoint of the line joining (5, 3) and (7, 7)? (a) (6, 5) (b) (12, 10) (c) (5, 6) (d) (1, 2)
  22. 22.In which quadrant does the point (1, 9) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  23. 23.What is the midpoint of the line joining (6, 10) and (8, 16)? (a) (1, 3) (b) (14, 26) (c) (7, 13) (d) (13, 7)
  24. 24.What is the distance between the points (7, 14) and (23, 2)? (a) 400 (b) 20 (c) 21 (d) 28
  25. 25.What is the distance between the points (7, 21) and (19, 5)? (a) 28 (b) 20 (c) 400 (d) 21
  26. 26.What is the distance between the points (9, 17) and (25, 5)? (a) 400 (b) 28 (c) 21 (d) 20
  27. 27.What is the distance between the points (8, 4) and (23, 12)? (a) 289 (b) 23 (c) 18 (d) 17
  28. 28.What is the distance between the points (1, 8) and (17, 20)? (a) 28 (b) 400 (c) 20 (d) 21
  29. 29.What is the midpoint of the line joining (5, 15) and (17, 3)? (a) (9, 11) (b) (6, 6) (c) (22, 18) (d) (11, 9)
  30. 30.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 16 (c) 225 (d) 15
  31. 31.What is the distance between the points (2, 23) and (10, 8)? (a) 17 (b) 18 (c) 23 (d) 289
  32. 32.What is the distance between the points (5, 6) and (8, 10)? (a) 6 (b) 7 (c) 5 (d) 25
  33. 33.In which quadrant does the point (1, −2) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  34. 34.What is the distance between the points (5, 8) and (14, 20)? (a) 16 (b) 15 (c) 225 (d) 21
  35. 35.What is the distance between the points (9, 14) and (21, 5)? (a) 21 (b) 16 (c) 225 (d) 15
  36. 36.What is the distance between the points (5, 4) and (9, 1)? (a) 6 (b) 7 (c) 25 (d) 5
  37. 37.What is the distance between the points (3, 0) and (8, 12)? (a) 169 (b) 14 (c) 17 (d) 13
  38. 38.What is the distance between the points (2, 0) and (14, 16)? (a) 21 (b) 28 (c) 400 (d) 20
  39. 39.What is the distance between the points (6, 0) and (10, 3)? (a) 25 (b) 7 (c) 6 (d) 5
  40. 40.How far is the point (12, 16) from the origin (0, 0)? (a) 20 (b) 28 (c) 21 (d) 400

Answer key

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

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