← Coordinates and distance lesson New set →

Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 874 · 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 (9, 12) from the origin (0, 0)? (a) 21 (b) 225 (c) 15 (d) 16
  2. 2.What is the distance between the points (6, 4) and (11, 16)? (a) 169 (b) 13 (c) 14 (d) 17
  3. 3.In which quadrant does the point (−9, 6) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  4. 4.What is the distance between the points (2, 26) and (9, 2)? (a) 31 (b) 26 (c) 25 (d) 625
  5. 5.What is the midpoint of the line joining (2, 1) and (14, 5)? (a) (6, 2) (b) (3, 8) (c) (16, 6) (d) (8, 3)
  6. 6.What is the midpoint of the line joining (10, 7) and (14, 3)? (a) (2, 2) (b) (24, 10) (c) (12, 5) (d) (5, 12)
  7. 7.What is the midpoint of the line joining (6, 8) and (18, 4)? (a) (12, 6) (b) (24, 12) (c) (6, 2) (d) (6, 12)
  8. 8.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 25 (c) 5 (d) 7
  9. 9.What is the midpoint of the line joining (10, 5) and (16, 1)? (a) (3, 2) (b) (3, 13) (c) (13, 3) (d) (26, 6)
  10. 10.How far is the point (24, 7) from the origin (0, 0)? (a) 26 (b) 25 (c) 625 (d) 31
  11. 11.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 31 (c) 25 (d) 625
  12. 12.In which quadrant does the point (−6, 5) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  13. 13.In which quadrant does the point (2, 1) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  14. 14.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 400 (c) 20 (d) 28
  15. 15.What is the midpoint of the line joining (10, 1) and (16, 5)? (a) (3, 2) (b) (13, 3) (c) (26, 6) (d) (3, 13)
  16. 16.In which quadrant does the point (7, −8) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  17. 17.In which quadrant does the point (−8, 1) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  18. 18.What is the midpoint of the line joining (6, 5) and (14, 9)? (a) (7, 10) (b) (20, 14) (c) (4, 2) (d) (10, 7)
  19. 19.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 14 (c) 169 (d) 13
  20. 20.What is the midpoint of the line joining (3, 9) and (9, 15)? (a) (3, 3) (b) (6, 12) (c) (12, 24) (d) (12, 6)
  21. 21.What is the midpoint of the line joining (4, 22) and (10, 10)? (a) (16, 7) (b) (7, 16) (c) (14, 32) (d) (3, 6)
  22. 22.What is the distance between the points (5, 0) and (8, 4)? (a) 6 (b) 7 (c) 25 (d) 5
  23. 23.What is the midpoint of the line joining (7, 12) and (15, 8)? (a) (10, 11) (b) (22, 20) (c) (11, 10) (d) (4, 2)
  24. 24.In which quadrant does the point (7, −7) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  25. 25.What is the distance between the points (5, 3) and (17, 19)? (a) 21 (b) 28 (c) 400 (d) 20
  26. 26.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 7 (c) 6 (d) 5
  27. 27.What is the midpoint of the line joining (7, 13) and (15, 3)? (a) (22, 16) (b) (11, 8) (c) (8, 11) (d) (4, 5)
  28. 28.What is the midpoint of the line joining (4, 16) and (16, 4)? (a) (20, 20) (b) (11, 10) (c) (6, 6) (d) (10, 10)
  29. 29.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 14 (c) 11 (d) 10
  30. 30.What is the midpoint of the line joining (8, 8) and (20, 4)? (a) (14, 6) (b) (28, 12) (c) (6, 2) (d) (6, 14)
  31. 31.What is the midpoint of the line joining (10, 2) and (18, 10)? (a) (6, 14) (b) (14, 6) (c) (4, 4) (d) (28, 12)
  32. 32.What is the distance between the points (0, 7) and (24, 14)? (a) 25 (b) 26 (c) 31 (d) 625
  33. 33.What is the distance between the points (6, 24) and (13, 0)? (a) 625 (b) 26 (c) 31 (d) 25
  34. 34.What is the distance between the points (7, 9) and (31, 2)? (a) 625 (b) 26 (c) 25 (d) 31
  35. 35.In which quadrant does the point (−7, 4) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  36. 36.What is the midpoint of the line joining (3, 12) and (15, 10)? (a) (11, 9) (b) (18, 22) (c) (6, 1) (d) (9, 11)
  37. 37.What is the distance between the points (0, 10) and (3, 6)? (a) 5 (b) 7 (c) 25 (d) 6
  38. 38.What is the midpoint of the line joining (7, 20) and (15, 10)? (a) (4, 5) (b) (22, 30) (c) (15, 11) (d) (11, 15)
  39. 39.In which quadrant does the point (9, 7) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  40. 40.How far is the point (12, 9) from the origin (0, 0)? (a) 16 (b) 21 (c) 15 (d) 225

Answer key

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

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