← Coordinates and distance lesson New set →

Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 460 · 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 (8, 15) and (10, 7)? (a) (9, 11) (b) (11, 9) (c) (1, 4) (d) (18, 22)
  2. 2.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 5 (c) 25 (d) 7
  3. 3.In which quadrant does the point (2, −5) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  4. 4.What is the midpoint of the line joining (3, 5) and (11, 17)? (a) (11, 7) (b) (14, 22) (c) (4, 6) (d) (7, 11)
  5. 5.In which quadrant does the point (1, −8) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  6. 6.What is the distance between the points (0, 9) and (24, 2)? (a) 26 (b) 31 (c) 25 (d) 625
  7. 7.In which quadrant does the point (7, −6) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  8. 8.What is the midpoint of the line joining (0, 20) and (4, 10)? (a) (4, 30) (b) (2, 5) (c) (15, 2) (d) (2, 15)
  9. 9.What is the distance between the points (0, 1) and (5, 13)? (a) 17 (b) 14 (c) 169 (d) 13
  10. 10.In which quadrant does the point (7, 5) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  11. 11.What is the midpoint of the line joining (2, 3) and (12, 1)? (a) (5, 1) (b) (7, 2) (c) (2, 7) (d) (14, 4)
  12. 12.In which quadrant does the point (2, −6) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  13. 13.What is the midpoint of the line joining (5, 6) and (11, 14)? (a) (16, 20) (b) (8, 10) (c) (10, 8) (d) (3, 4)
  14. 14.What is the distance between the points (4, 0) and (12, 6)? (a) 10 (b) 100 (c) 11 (d) 14
  15. 15.What is the distance between the points (1, 2) and (9, 8)? (a) 100 (b) 11 (c) 14 (d) 10
  16. 16.What is the midpoint of the line joining (6, 13) and (16, 5)? (a) (9, 11) (b) (11, 9) (c) (5, 4) (d) (22, 18)
  17. 17.What is the midpoint of the line joining (8, 3) and (10, 1)? (a) (2, 9) (b) (18, 4) (c) (9, 2) (d) (1, 1)
  18. 18.In which quadrant does the point (3, 9) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  19. 19.What is the distance between the points (2, 9) and (18, 21)? (a) 28 (b) 21 (c) 20 (d) 400
  20. 20.What is the distance between the points (1, 7) and (5, 4)? (a) 7 (b) 6 (c) 5 (d) 25
  21. 21.What is the distance between the points (5, 12) and (21, 0)? (a) 20 (b) 28 (c) 21 (d) 400
  22. 22.In which quadrant does the point (−8, 9) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  23. 23.What is the distance between the points (7, 5) and (19, 0)? (a) 13 (b) 169 (c) 17 (d) 14
  24. 24.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 18 (c) 289 (d) 17
  25. 25.What is the distance between the points (1, 0) and (4, 4)? (a) 7 (b) 25 (c) 5 (d) 6
  26. 26.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 14 (c) 13 (d) 17
  27. 27.What is the distance between the points (7, 0) and (22, 8)? (a) 23 (b) 17 (c) 289 (d) 18
  28. 28.What is the midpoint of the line joining (9, 17) and (13, 9)? (a) (11, 13) (b) (22, 26) (c) (13, 11) (d) (2, 4)
  29. 29.What is the distance between the points (2, 14) and (17, 6)? (a) 18 (b) 289 (c) 23 (d) 17
  30. 30.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 625 (c) 26 (d) 25
  31. 31.What is the midpoint of the line joining (5, 17) and (9, 5)? (a) (7, 11) (b) (11, 7) (c) (2, 6) (d) (14, 22)
  32. 32.What is the midpoint of the line joining (2, 4) and (12, 12)? (a) (8, 7) (b) (5, 4) (c) (7, 8) (d) (14, 16)
  33. 33.In which quadrant does the point (4, 7) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  34. 34.What is the midpoint of the line joining (7, 13) and (17, 7)? (a) (10, 12) (b) (12, 10) (c) (24, 20) (d) (5, 3)
  35. 35.What is the distance between the points (1, 6) and (9, 21)? (a) 18 (b) 17 (c) 23 (d) 289
  36. 36.What is the distance between the points (2, 3) and (26, 10)? (a) 31 (b) 25 (c) 625 (d) 26
  37. 37.What is the distance between the points (2, 21) and (18, 9)? (a) 28 (b) 20 (c) 400 (d) 21
  38. 38.What is the distance between the points (7, 3) and (14, 27)? (a) 25 (b) 26 (c) 31 (d) 625
  39. 39.In which quadrant does the point (1, 6) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  40. 40.In which quadrant does the point (1, 1) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant

Answer key

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

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