← Coordinates and distance lesson New set →

Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 98 · 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 (5, 1) and (15, 5)? (a) (3, 10) (b) (5, 2) (c) (20, 6) (d) (10, 3)
  2. 2.What is the midpoint of the line joining (4, 3) and (8, 1)? (a) (2, 1) (b) (6, 2) (c) (2, 6) (d) (12, 4)
  3. 3.What is the distance between the points (7, 5) and (12, 17)? (a) 17 (b) 14 (c) 13 (d) 169
  4. 4.What is the distance between the points (6, 17) and (15, 5)? (a) 225 (b) 21 (c) 15 (d) 16
  5. 5.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 11 (c) 100 (d) 14
  6. 6.What is the distance between the points (7, 1) and (31, 8)? (a) 26 (b) 31 (c) 625 (d) 25
  7. 7.In which quadrant does the point (1, 1) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  8. 8.What is the distance between the points (1, 7) and (7, 15)? (a) 11 (b) 100 (c) 10 (d) 14
  9. 9.What is the distance between the points (8, 4) and (20, 13)? (a) 16 (b) 15 (c) 21 (d) 225
  10. 10.What is the distance between the points (5, 8) and (9, 11)? (a) 25 (b) 7 (c) 5 (d) 6
  11. 11.What is the distance between the points (9, 10) and (24, 2)? (a) 289 (b) 23 (c) 18 (d) 17
  12. 12.What is the distance between the points (8, 15) and (20, 6)? (a) 15 (b) 21 (c) 16 (d) 225
  13. 13.What is the midpoint of the line joining (9, 12) and (15, 0)? (a) (12, 6) (b) (24, 12) (c) (6, 12) (d) (3, 6)
  14. 14.What is the midpoint of the line joining (3, 14) and (11, 4)? (a) (9, 7) (b) (4, 5) (c) (14, 18) (d) (7, 9)
  15. 15.What is the distance between the points (1, 10) and (5, 7)? (a) 7 (b) 25 (c) 6 (d) 5
  16. 16.What is the midpoint of the line joining (10, 8) and (18, 2)? (a) (5, 14) (b) (14, 5) (c) (28, 10) (d) (4, 3)
  17. 17.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 289 (c) 17 (d) 23
  18. 18.What is the midpoint of the line joining (0, 7) and (2, 13)? (a) (2, 20) (b) (1, 3) (c) (1, 10) (d) (10, 1)
  19. 19.What is the midpoint of the line joining (3, 2) and (5, 14)? (a) (1, 6) (b) (8, 4) (c) (8, 16) (d) (4, 8)
  20. 20.What is the distance between the points (7, 5) and (19, 21)? (a) 20 (b) 21 (c) 400 (d) 28
  21. 21.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 28 (c) 400 (d) 20
  22. 22.In which quadrant does the point (8, −3) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  23. 23.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 225 (c) 15 (d) 16
  24. 24.In which quadrant does the point (2, 5) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  25. 25.In which quadrant does the point (6, 8) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  26. 26.How far is the point (7, 24) from the origin (0, 0)? (a) 25 (b) 26 (c) 31 (d) 625
  27. 27.What is the distance between the points (5, 15) and (10, 3)? (a) 17 (b) 169 (c) 14 (d) 13
  28. 28.In which quadrant does the point (−1, 7) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  29. 29.What is the midpoint of the line joining (9, 20) and (15, 8)? (a) (12, 14) (b) (24, 28) (c) (3, 6) (d) (14, 12)
  30. 30.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 169 (c) 17 (d) 13
  31. 31.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 10 (c) 11 (d) 14
  32. 32.In which quadrant does the point (−6, −5) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  33. 33.In which quadrant does the point (−8, −6) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  34. 34.What is the distance between the points (8, 10) and (12, 7)? (a) 5 (b) 6 (c) 25 (d) 7
  35. 35.What is the midpoint of the line joining (3, 13) and (5, 3)? (a) (8, 16) (b) (4, 8) (c) (8, 4) (d) (1, 5)
  36. 36.In which quadrant does the point (−5, 4) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  37. 37.What is the midpoint of the line joining (3, 8) and (7, 4)? (a) (2, 2) (b) (5, 6) (c) (10, 12) (d) (6, 5)
  38. 38.In which quadrant does the point (−3, 6) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  39. 39.In which quadrant does the point (9, 5) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  40. 40.What is the distance between the points (5, 6) and (10, 18)? (a) 13 (b) 17 (c) 169 (d) 14

Answer key

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

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