← Coordinates and distance lesson New set →

Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 616 · 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, 22) and (13, 10)? (a) (16, 10) (b) (20, 32) (c) (3, 6) (d) (10, 16)
  2. 2.What is the midpoint of the line joining (9, 9) and (21, 7)? (a) (15, 8) (b) (6, 1) (c) (30, 16) (d) (8, 15)
  3. 3.What is the midpoint of the line joining (6, 5) and (10, 11)? (a) (16, 16) (b) (2, 3) (c) (8, 8) (d) (9, 8)
  4. 4.What is the midpoint of the line joining (6, 1) and (14, 13)? (a) (7, 10) (b) (4, 6) (c) (10, 7) (d) (20, 14)
  5. 5.What is the midpoint of the line joining (2, 12) and (14, 4)? (a) (6, 4) (b) (9, 8) (c) (8, 8) (d) (16, 16)
  6. 6.What is the distance between the points (5, 10) and (17, 1)? (a) 225 (b) 15 (c) 16 (d) 21
  7. 7.What is the midpoint of the line joining (8, 11) and (18, 1)? (a) (26, 12) (b) (5, 5) (c) (13, 6) (d) (6, 13)
  8. 8.What is the midpoint of the line joining (2, 18) and (12, 8)? (a) (5, 5) (b) (7, 13) (c) (14, 26) (d) (13, 7)
  9. 9.What is the distance between the points (2, 4) and (9, 28)? (a) 625 (b) 26 (c) 31 (d) 25
  10. 10.What is the midpoint of the line joining (8, 16) and (20, 8)? (a) (14, 12) (b) (6, 4) (c) (28, 24) (d) (12, 14)
  11. 11.In which quadrant does the point (−7, −1) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  12. 12.What is the midpoint of the line joining (7, 15) and (9, 5)? (a) (8, 10) (b) (1, 5) (c) (16, 20) (d) (10, 8)
  13. 13.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 625 (c) 26 (d) 25
  14. 14.What is the distance between the points (5, 19) and (17, 3)? (a) 400 (b) 28 (c) 21 (d) 20
  15. 15.What is the midpoint of the line joining (10, 5) and (18, 17)? (a) (11, 14) (b) (28, 22) (c) (4, 6) (d) (14, 11)
  16. 16.What is the midpoint of the line joining (0, 9) and (12, 13)? (a) (6, 2) (b) (11, 6) (c) (12, 22) (d) (6, 11)
  17. 17.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 5 (c) 7 (d) 6
  18. 18.What is the distance between the points (1, 15) and (17, 3)? (a) 28 (b) 400 (c) 20 (d) 21
  19. 19.What is the distance between the points (0, 3) and (9, 15)? (a) 16 (b) 15 (c) 225 (d) 21
  20. 20.What is the distance between the points (5, 13) and (14, 1)? (a) 16 (b) 15 (c) 225 (d) 21
  21. 21.What is the distance between the points (5, 17) and (14, 5)? (a) 15 (b) 21 (c) 16 (d) 225
  22. 22.In which quadrant does the point (4, −5) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  23. 23.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 400 (c) 20 (d) 28
  24. 24.What is the distance between the points (1, 7) and (4, 3)? (a) 6 (b) 7 (c) 5 (d) 25
  25. 25.What is the distance between the points (3, 9) and (27, 16)? (a) 625 (b) 31 (c) 26 (d) 25
  26. 26.In which quadrant does the point (7, 2) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  27. 27.In which quadrant does the point (−8, 9) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  28. 28.In which quadrant does the point (2, −8) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  29. 29.What is the midpoint of the line joining (0, 9) and (2, 7)? (a) (1, 1) (b) (1, 8) (c) (2, 16) (d) (8, 1)
  30. 30.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 23 (c) 17 (d) 18
  31. 31.What is the midpoint of the line joining (3, 11) and (7, 5)? (a) (10, 16) (b) (5, 8) (c) (2, 3) (d) (8, 5)
  32. 32.What is the distance between the points (0, 3) and (12, 8)? (a) 169 (b) 13 (c) 17 (d) 14
  33. 33.What is the distance between the points (5, 2) and (17, 11)? (a) 15 (b) 16 (c) 21 (d) 225
  34. 34.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 100 (c) 14 (d) 10
  35. 35.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 31 (c) 25 (d) 26
  36. 36.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 13 (c) 14 (d) 169
  37. 37.What is the midpoint of the line joining (2, 6) and (4, 4)? (a) (1, 1) (b) (5, 3) (c) (3, 5) (d) (6, 10)
  38. 38.What is the distance between the points (8, 1) and (16, 7)? (a) 14 (b) 100 (c) 11 (d) 10
  39. 39.What is the distance between the points (1, 21) and (9, 6)? (a) 23 (b) 17 (c) 18 (d) 289
  40. 40.In which quadrant does the point (−1, −9) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant

Answer key

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

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