← Coordinates and distance lesson New set →

Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 797 · 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, 8) and (8, 14)? (a) (3, 3) (b) (5, 11) (c) (11, 5) (d) (10, 22)
  2. 2.What is the distance between the points (7, 20) and (23, 8)? (a) 21 (b) 400 (c) 28 (d) 20
  3. 3.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 100 (c) 10 (d) 14
  4. 4.What is the distance between the points (3, 2) and (6, 6)? (a) 25 (b) 7 (c) 6 (d) 5
  5. 5.What is the midpoint of the line joining (1, 1) and (5, 11)? (a) (6, 3) (b) (2, 5) (c) (3, 6) (d) (6, 12)
  6. 6.In which quadrant does the point (6, −8) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  7. 7.In which quadrant does the point (1, −2) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  8. 8.What is the distance between the points (3, 7) and (10, 31)? (a) 625 (b) 31 (c) 26 (d) 25
  9. 9.What is the midpoint of the line joining (4, 6) and (6, 18)? (a) (1, 6) (b) (12, 5) (c) (10, 24) (d) (5, 12)
  10. 10.What is the distance between the points (6, 12) and (18, 7)? (a) 169 (b) 17 (c) 14 (d) 13
  11. 11.What is the midpoint of the line joining (3, 4) and (9, 10)? (a) (7, 6) (b) (12, 14) (c) (3, 3) (d) (6, 7)
  12. 12.What is the distance between the points (1, 1) and (13, 10)? (a) 16 (b) 225 (c) 21 (d) 15
  13. 13.What is the distance between the points (7, 1) and (13, 9)? (a) 11 (b) 100 (c) 14 (d) 10
  14. 14.In which quadrant does the point (5, 7) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  15. 15.What is the midpoint of the line joining (5, 14) and (7, 2)? (a) (1, 6) (b) (8, 6) (c) (12, 16) (d) (6, 8)
  16. 16.What is the midpoint of the line joining (9, 5) and (21, 1)? (a) (3, 15) (b) (15, 3) (c) (6, 2) (d) (30, 6)
  17. 17.What is the distance between the points (5, 8) and (29, 1)? (a) 625 (b) 31 (c) 25 (d) 26
  18. 18.What is the midpoint of the line joining (7, 5) and (15, 7)? (a) (6, 11) (b) (11, 6) (c) (4, 1) (d) (22, 12)
  19. 19.In which quadrant does the point (−5, −7) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  20. 20.In which quadrant does the point (9, 3) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  21. 21.What is the midpoint of the line joining (4, 13) and (14, 7)? (a) (5, 3) (b) (18, 20) (c) (9, 10) (d) (10, 9)
  22. 22.What is the distance between the points (9, 8) and (12, 12)? (a) 7 (b) 6 (c) 25 (d) 5
  23. 23.In which quadrant does the point (−9, 4) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  24. 24.In which quadrant does the point (6, −4) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  25. 25.What is the distance between the points (2, 0) and (6, 3)? (a) 6 (b) 7 (c) 5 (d) 25
  26. 26.What is the midpoint of the line joining (10, 6) and (16, 16)? (a) (11, 13) (b) (3, 5) (c) (13, 11) (d) (26, 22)
  27. 27.What is the distance between the points (2, 5) and (17, 13)? (a) 289 (b) 23 (c) 17 (d) 18
  28. 28.What is the distance between the points (8, 1) and (15, 25)? (a) 25 (b) 625 (c) 26 (d) 31
  29. 29.In which quadrant does the point (3, −7) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  30. 30.What is the distance between the points (9, 29) and (16, 5)? (a) 25 (b) 625 (c) 26 (d) 31
  31. 31.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 7 (c) 6 (d) 5
  32. 32.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 17 (c) 14 (d) 13
  33. 33.What is the distance between the points (3, 4) and (9, 12)? (a) 11 (b) 14 (c) 100 (d) 10
  34. 34.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 289 (c) 18 (d) 17
  35. 35.In which quadrant does the point (4, 8) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  36. 36.What is the midpoint of the line joining (3, 2) and (7, 4)? (a) (10, 6) (b) (5, 3) (c) (3, 5) (d) (2, 1)
  37. 37.What is the distance between the points (4, 27) and (11, 3)? (a) 625 (b) 25 (c) 31 (d) 26
  38. 38.What is the distance between the points (1, 8) and (13, 17)? (a) 15 (b) 21 (c) 225 (d) 16
  39. 39.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 20 (c) 28 (d) 400
  40. 40.What is the midpoint of the line joining (3, 15) and (7, 9)? (a) (10, 24) (b) (2, 3) (c) (12, 5) (d) (5, 12)

Answer key

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

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