← Coordinates and distance lesson New set →

Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 296 · 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 midpoint of the line joining (2, 7) and (14, 3)? (a) (5, 8) (b) (16, 10) (c) (8, 5) (d) (6, 2)
  2. 2.What is the midpoint of the line joining (2, 6) and (6, 16)? (a) (4, 11) (b) (2, 5) (c) (11, 4) (d) (8, 22)
  3. 3.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 6 (c) 25 (d) 5
  4. 4.What is the distance between the points (2, 19) and (10, 4)? (a) 289 (b) 18 (c) 23 (d) 17
  5. 5.What is the distance between the points (0, 6) and (8, 12)? (a) 14 (b) 10 (c) 11 (d) 100
  6. 6.In which quadrant does the point (4, 3) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  7. 7.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 26 (c) 625 (d) 25
  8. 8.What is the distance between the points (8, 11) and (11, 7)? (a) 6 (b) 25 (c) 7 (d) 5
  9. 9.What is the distance between the points (1, 4) and (9, 10)? (a) 14 (b) 100 (c) 10 (d) 11
  10. 10.What is the midpoint of the line joining (6, 3) and (10, 5)? (a) (8, 4) (b) (4, 8) (c) (2, 1) (d) (16, 8)
  11. 11.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 18 (c) 23 (d) 289
  12. 12.What is the distance between the points (0, 18) and (9, 6)? (a) 16 (b) 21 (c) 15 (d) 225
  13. 13.What is the midpoint of the line joining (4, 6) and (16, 0)? (a) (20, 6) (b) (10, 3) (c) (6, 3) (d) (3, 10)
  14. 14.What is the midpoint of the line joining (2, 17) and (10, 9)? (a) (13, 6) (b) (4, 4) (c) (12, 26) (d) (6, 13)
  15. 15.What is the midpoint of the line joining (8, 6) and (14, 0)? (a) (3, 11) (b) (11, 3) (c) (3, 3) (d) (22, 6)
  16. 16.In which quadrant does the point (2, −1) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  17. 17.What is the midpoint of the line joining (6, 4) and (10, 16)? (a) (8, 10) (b) (16, 20) (c) (10, 8) (d) (2, 6)
  18. 18.What is the midpoint of the line joining (1, 12) and (9, 2)? (a) (7, 5) (b) (10, 14) (c) (4, 5) (d) (5, 7)
  19. 19.What is the distance between the points (3, 0) and (15, 5)? (a) 169 (b) 13 (c) 17 (d) 14
  20. 20.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 625 (c) 26 (d) 25
  21. 21.In which quadrant does the point (9, 1) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  22. 22.What is the distance between the points (5, 7) and (20, 15)? (a) 289 (b) 18 (c) 23 (d) 17
  23. 23.What is the distance between the points (2, 23) and (10, 8)? (a) 289 (b) 18 (c) 17 (d) 23
  24. 24.What is the distance between the points (8, 25) and (20, 9)? (a) 21 (b) 28 (c) 20 (d) 400
  25. 25.What is the distance between the points (8, 9) and (15, 33)? (a) 26 (b) 25 (c) 625 (d) 31
  26. 26.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 21 (c) 16 (d) 15
  27. 27.In which quadrant does the point (−2, −2) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  28. 28.In which quadrant does the point (−8, −1) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  29. 29.In which quadrant does the point (−2, −7) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  30. 30.What is the distance between the points (4, 29) and (11, 5)? (a) 625 (b) 31 (c) 26 (d) 25
  31. 31.What is the distance between the points (2, 12) and (14, 3)? (a) 16 (b) 15 (c) 225 (d) 21
  32. 32.What is the distance between the points (6, 7) and (18, 16)? (a) 16 (b) 15 (c) 225 (d) 21
  33. 33.What is the distance between the points (6, 7) and (15, 19)? (a) 16 (b) 15 (c) 225 (d) 21
  34. 34.What is the midpoint of the line joining (5, 1) and (11, 5)? (a) (8, 3) (b) (16, 6) (c) (3, 2) (d) (3, 8)
  35. 35.What is the midpoint of the line joining (9, 1) and (13, 13)? (a) (2, 6) (b) (11, 7) (c) (22, 14) (d) (7, 11)
  36. 36.What is the distance between the points (9, 7) and (12, 11)? (a) 5 (b) 6 (c) 25 (d) 7
  37. 37.What is the midpoint of the line joining (1, 4) and (7, 0)? (a) (2, 4) (b) (3, 2) (c) (4, 2) (d) (8, 4)
  38. 38.In which quadrant does the point (−6, 5) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  39. 39.What is the distance between the points (4, 14) and (19, 6)? (a) 18 (b) 289 (c) 17 (d) 23
  40. 40.In which quadrant does the point (1, 7) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant

Answer key

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

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