← Coordinates and distance lesson New set →

Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 745 · 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 (7, 8) and (19, 4)? (a) (26, 12) (b) (13, 6) (c) (6, 13) (d) (6, 2)
  2. 2.What is the distance between the points (6, 5) and (10, 8)? (a) 5 (b) 25 (c) 7 (d) 6
  3. 3.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 225 (c) 15 (d) 16
  4. 4.What is the midpoint of the line joining (7, 1) and (9, 11)? (a) (6, 8) (b) (1, 5) (c) (16, 12) (d) (8, 6)
  5. 5.What is the distance between the points (5, 2) and (9, 5)? (a) 7 (b) 6 (c) 25 (d) 5
  6. 6.What is the midpoint of the line joining (0, 6) and (8, 12)? (a) (4, 3) (b) (9, 4) (c) (4, 9) (d) (8, 18)
  7. 7.In which quadrant does the point (6, 8) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  8. 8.What is the distance between the points (8, 33) and (15, 9)? (a) 25 (b) 26 (c) 31 (d) 625
  9. 9.What is the midpoint of the line joining (2, 6) and (10, 2)? (a) (4, 2) (b) (12, 8) (c) (4, 6) (d) (6, 4)
  10. 10.What is the distance between the points (8, 0) and (24, 12)? (a) 20 (b) 21 (c) 400 (d) 28
  11. 11.What is the distance between the points (9, 15) and (17, 9)? (a) 11 (b) 10 (c) 14 (d) 100
  12. 12.What is the distance between the points (2, 7) and (6, 10)? (a) 6 (b) 25 (c) 5 (d) 7
  13. 13.What is the distance between the points (0, 4) and (5, 16)? (a) 169 (b) 13 (c) 14 (d) 17
  14. 14.What is the distance between the points (0, 0) and (7, 24)? (a) 31 (b) 625 (c) 26 (d) 25
  15. 15.What is the distance between the points (4, 5) and (8, 8)? (a) 7 (b) 25 (c) 5 (d) 6
  16. 16.In which quadrant does the point (3, −4) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  17. 17.What is the midpoint of the line joining (2, 10) and (8, 0)? (a) (10, 10) (b) (5, 5) (c) (6, 5) (d) (3, 5)
  18. 18.What is the midpoint of the line joining (7, 16) and (9, 6)? (a) (8, 11) (b) (16, 22) (c) (11, 8) (d) (1, 5)
  19. 19.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 17 (c) 18 (d) 289
  20. 20.What is the distance between the points (5, 14) and (10, 2)? (a) 13 (b) 169 (c) 14 (d) 17
  21. 21.What is the midpoint of the line joining (0, 3) and (2, 15)? (a) (1, 6) (b) (2, 18) (c) (1, 9) (d) (9, 1)
  22. 22.In which quadrant does the point (4, −8) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  23. 23.What is the distance between the points (9, 12) and (21, 7)? (a) 169 (b) 13 (c) 17 (d) 14
  24. 24.What is the midpoint of the line joining (8, 3) and (12, 9)? (a) (20, 12) (b) (2, 3) (c) (10, 6) (d) (6, 10)
  25. 25.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 25 (c) 5 (d) 6
  26. 26.What is the distance between the points (7, 7) and (15, 22)? (a) 17 (b) 23 (c) 18 (d) 289
  27. 27.What is the distance between the points (4, 5) and (16, 10)? (a) 14 (b) 13 (c) 17 (d) 169
  28. 28.What is the midpoint of the line joining (10, 2) and (18, 14)? (a) (14, 8) (b) (4, 6) (c) (28, 16) (d) (8, 14)
  29. 29.What is the distance between the points (9, 2) and (18, 14)? (a) 21 (b) 16 (c) 225 (d) 15
  30. 30.What is the distance between the points (0, 2) and (24, 9)? (a) 26 (b) 25 (c) 625 (d) 31
  31. 31.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 14 (c) 10 (d) 100
  32. 32.What is the distance between the points (9, 22) and (17, 7)? (a) 23 (b) 18 (c) 289 (d) 17
  33. 33.In which quadrant does the point (−9, 3) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  34. 34.What is the distance between the points (3, 4) and (15, 20)? (a) 400 (b) 21 (c) 28 (d) 20
  35. 35.What is the midpoint of the line joining (3, 1) and (7, 9)? (a) (10, 10) (b) (6, 5) (c) (5, 5) (d) (2, 4)
  36. 36.What is the midpoint of the line joining (3, 5) and (13, 7)? (a) (16, 12) (b) (5, 1) (c) (6, 8) (d) (8, 6)
  37. 37.What is the midpoint of the line joining (1, 10) and (13, 20)? (a) (15, 7) (b) (6, 5) (c) (14, 30) (d) (7, 15)
  38. 38.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 15 (c) 16 (d) 225
  39. 39.What is the distance between the points (8, 12) and (24, 0)? (a) 21 (b) 28 (c) 400 (d) 20
  40. 40.What is the distance between the points (2, 2) and (8, 10)? (a) 11 (b) 100 (c) 10 (d) 14

Answer key

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

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