← Coordinates and distance lesson New set →

Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 718 · 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.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 10 (c) 100 (d) 14
  2. 2.What is the midpoint of the line joining (8, 0) and (20, 4)? (a) (6, 2) (b) (2, 14) (c) (28, 4) (d) (14, 2)
  3. 3.In which quadrant does the point (8, −6) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  4. 4.What is the midpoint of the line joining (9, 12) and (13, 8)? (a) (2, 2) (b) (11, 10) (c) (22, 20) (d) (10, 11)
  5. 5.What is the midpoint of the line joining (4, 9) and (14, 7)? (a) (5, 1) (b) (8, 9) (c) (18, 16) (d) (9, 8)
  6. 6.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 31 (c) 26 (d) 25
  7. 7.In which quadrant does the point (6, 7) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  8. 8.In which quadrant does the point (1, 2) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  9. 9.In which quadrant does the point (−3, 9) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  10. 10.What is the distance between the points (9, 9) and (24, 17)? (a) 289 (b) 17 (c) 23 (d) 18
  11. 11.In which quadrant does the point (8, 1) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  12. 12.What is the distance between the points (1, 7) and (7, 15)? (a) 11 (b) 14 (c) 10 (d) 100
  13. 13.In which quadrant does the point (−2, −5) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  14. 14.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 7 (c) 5 (d) 25
  15. 15.In which quadrant does the point (2, −2) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  16. 16.What is the midpoint of the line joining (6, 8) and (10, 0)? (a) (16, 8) (b) (8, 4) (c) (4, 8) (d) (2, 4)
  17. 17.What is the midpoint of the line joining (10, 5) and (12, 9)? (a) (11, 7) (b) (7, 11) (c) (22, 14) (d) (1, 2)
  18. 18.What is the midpoint of the line joining (6, 6) and (14, 12)? (a) (20, 18) (b) (4, 3) (c) (10, 9) (d) (9, 10)
  19. 19.What is the distance between the points (0, 8) and (6, 0)? (a) 11 (b) 100 (c) 10 (d) 14
  20. 20.What is the midpoint of the line joining (7, 10) and (15, 12)? (a) (22, 22) (b) (4, 1) (c) (11, 11) (d) (12, 11)
  21. 21.What is the distance between the points (7, 22) and (15, 7)? (a) 23 (b) 289 (c) 18 (d) 17
  22. 22.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 28 (c) 20 (d) 400
  23. 23.In which quadrant does the point (7, −1) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  24. 24.What is the midpoint of the line joining (6, 0) and (16, 2)? (a) (5, 1) (b) (11, 1) (c) (1, 11) (d) (22, 2)
  25. 25.In which quadrant does the point (7, 3) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  26. 26.What is the distance between the points (4, 8) and (13, 20)? (a) 21 (b) 15 (c) 16 (d) 225
  27. 27.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 18 (c) 23 (d) 17
  28. 28.What is the distance between the points (2, 21) and (11, 9)? (a) 15 (b) 225 (c) 16 (d) 21
  29. 29.What is the midpoint of the line joining (6, 1) and (14, 5)? (a) (4, 2) (b) (3, 10) (c) (20, 6) (d) (10, 3)
  30. 30.What is the distance between the points (6, 5) and (12, 13)? (a) 11 (b) 100 (c) 10 (d) 14
  31. 31.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 13 (c) 17 (d) 14
  32. 32.What is the distance between the points (4, 13) and (28, 6)? (a) 25 (b) 625 (c) 26 (d) 31
  33. 33.What is the distance between the points (2, 0) and (7, 12)? (a) 14 (b) 169 (c) 17 (d) 13
  34. 34.What is the distance between the points (7, 2) and (14, 26)? (a) 31 (b) 625 (c) 26 (d) 25
  35. 35.What is the midpoint of the line joining (4, 1) and (12, 5)? (a) (3, 8) (b) (4, 2) (c) (16, 6) (d) (8, 3)
  36. 36.In which quadrant does the point (3, 4) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  37. 37.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 16 (c) 15 (d) 225
  38. 38.What is the midpoint of the line joining (5, 3) and (9, 1)? (a) (2, 1) (b) (14, 4) (c) (7, 2) (d) (2, 7)
  39. 39.How far is the point (24, 7) from the origin (0, 0)? (a) 26 (b) 625 (c) 31 (d) 25
  40. 40.What is the midpoint of the line joining (9, 8) and (15, 6)? (a) (12, 7) (b) (3, 1) (c) (24, 14) (d) (7, 12)

Answer key

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

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