← Coordinates and distance lesson New set →

Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 72 · 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 (15, 8) from the origin (0, 0)? (a) 23 (b) 18 (c) 289 (d) 17
  2. 2.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 7 (c) 6 (d) 5
  3. 3.What is the distance between the points (6, 3) and (22, 15)? (a) 21 (b) 400 (c) 20 (d) 28
  4. 4.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 13 (c) 17 (d) 169
  5. 5.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 625 (c) 25 (d) 26
  6. 6.In which quadrant does the point (7, 3) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  7. 7.What is the midpoint of the line joining (8, 7) and (14, 13)? (a) (10, 11) (b) (22, 20) (c) (3, 3) (d) (11, 10)
  8. 8.In which quadrant does the point (5, 6) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  9. 9.In which quadrant does the point (5, 5) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  10. 10.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 15 (c) 225 (d) 16
  11. 11.What is the distance between the points (0, 8) and (8, 2)? (a) 100 (b) 10 (c) 14 (d) 11
  12. 12.How far is the point (12, 16) from the origin (0, 0)? (a) 20 (b) 28 (c) 400 (d) 21
  13. 13.How far is the point (4, 3) from the origin (0, 0)? (a) 5 (b) 6 (c) 25 (d) 7
  14. 14.What is the distance between the points (4, 9) and (8, 6)? (a) 5 (b) 7 (c) 25 (d) 6
  15. 15.What is the distance between the points (1, 22) and (9, 7)? (a) 18 (b) 289 (c) 17 (d) 23
  16. 16.In which quadrant does the point (1, 1) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  17. 17.What is the distance between the points (7, 8) and (13, 0)? (a) 10 (b) 11 (c) 14 (d) 100
  18. 18.In which quadrant does the point (−3, 9) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  19. 19.What is the midpoint of the line joining (10, 17) and (14, 9)? (a) (13, 12) (b) (2, 4) (c) (24, 26) (d) (12, 13)
  20. 20.What is the midpoint of the line joining (6, 6) and (14, 2)? (a) (4, 2) (b) (10, 4) (c) (4, 10) (d) (20, 8)
  21. 21.What is the distance between the points (2, 0) and (14, 16)? (a) 400 (b) 28 (c) 20 (d) 21
  22. 22.How far is the point (12, 5) from the origin (0, 0)? (a) 13 (b) 169 (c) 17 (d) 14
  23. 23.What is the midpoint of the line joining (4, 11) and (16, 1)? (a) (20, 12) (b) (10, 6) (c) (6, 5) (d) (6, 10)
  24. 24.What is the midpoint of the line joining (9, 5) and (19, 3)? (a) (4, 14) (b) (28, 8) (c) (5, 1) (d) (14, 4)
  25. 25.What is the distance between the points (4, 7) and (11, 31)? (a) 25 (b) 26 (c) 31 (d) 625
  26. 26.What is the midpoint of the line joining (2, 2) and (4, 8)? (a) (6, 10) (b) (3, 5) (c) (5, 3) (d) (1, 3)
  27. 27.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 23 (c) 289 (d) 17
  28. 28.What is the distance between the points (7, 33) and (14, 9)? (a) 26 (b) 625 (c) 31 (d) 25
  29. 29.What is the midpoint of the line joining (5, 0) and (7, 12)? (a) (6, 6) (b) (1, 6) (c) (7, 6) (d) (12, 12)
  30. 30.In which quadrant does the point (−3, 5) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  31. 31.In which quadrant does the point (−6, −2) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  32. 32.What is the midpoint of the line joining (5, 6) and (7, 14)? (a) (1, 4) (b) (12, 20) (c) (10, 6) (d) (6, 10)
  33. 33.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 21 (c) 16 (d) 15
  34. 34.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 100 (c) 11 (d) 10
  35. 35.What is the distance between the points (5, 0) and (13, 15)? (a) 289 (b) 17 (c) 23 (d) 18
  36. 36.In which quadrant does the point (−1, 2) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  37. 37.In which quadrant does the point (−9, 7) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  38. 38.What is the midpoint of the line joining (0, 6) and (2, 2)? (a) (4, 1) (b) (2, 8) (c) (1, 4) (d) (1, 2)
  39. 39.In which quadrant does the point (−4, −7) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  40. 40.What is the distance between the points (0, 12) and (6, 4)? (a) 100 (b) 10 (c) 11 (d) 14

Answer key

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

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