← Coordinates and distance lesson New set →

Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 191 · 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.In which quadrant does the point (−5, 3) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  2. 2.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 16 (c) 15 (d) 225
  3. 3.What is the distance between the points (6, 10) and (18, 1)? (a) 21 (b) 16 (c) 225 (d) 15
  4. 4.What is the midpoint of the line joining (2, 15) and (14, 3)? (a) (6, 6) (b) (9, 8) (c) (8, 9) (d) (16, 18)
  5. 5.How far is the point (4, 3) from the origin (0, 0)? (a) 5 (b) 6 (c) 7 (d) 25
  6. 6.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 5 (c) 25 (d) 7
  7. 7.In which quadrant does the point (−8, 9) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  8. 8.In which quadrant does the point (−2, 7) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  9. 9.What is the distance between the points (0, 10) and (3, 6)? (a) 7 (b) 6 (c) 5 (d) 25
  10. 10.What is the distance between the points (7, 15) and (31, 8)? (a) 26 (b) 25 (c) 625 (d) 31
  11. 11.How far is the point (24, 7) from the origin (0, 0)? (a) 26 (b) 625 (c) 31 (d) 25
  12. 12.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 100 (c) 10 (d) 11
  13. 13.What is the midpoint of the line joining (10, 12) and (22, 6)? (a) (32, 18) (b) (16, 9) (c) (6, 3) (d) (9, 16)
  14. 14.In which quadrant does the point (−6, 3) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  15. 15.In which quadrant does the point (1, 8) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  16. 16.In which quadrant does the point (6, −8) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  17. 17.What is the distance between the points (8, 4) and (12, 7)? (a) 5 (b) 7 (c) 25 (d) 6
  18. 18.What is the distance between the points (3, 14) and (9, 6)? (a) 100 (b) 10 (c) 11 (d) 14
  19. 19.In which quadrant does the point (8, 2) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  20. 20.What is the midpoint of the line joining (6, 3) and (16, 7)? (a) (5, 2) (b) (22, 10) (c) (11, 5) (d) (5, 11)
  21. 21.What is the distance between the points (7, 3) and (23, 15)? (a) 20 (b) 28 (c) 400 (d) 21
  22. 22.What is the distance between the points (9, 0) and (12, 4)? (a) 7 (b) 6 (c) 25 (d) 5
  23. 23.In which quadrant does the point (3, −8) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  24. 24.What is the distance between the points (6, 5) and (18, 0)? (a) 13 (b) 14 (c) 169 (d) 17
  25. 25.In which quadrant does the point (−9, 1) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  26. 26.What is the midpoint of the line joining (2, 10) and (8, 8)? (a) (10, 18) (b) (9, 5) (c) (3, 1) (d) (5, 9)
  27. 27.What is the midpoint of the line joining (7, 5) and (9, 1)? (a) (8, 3) (b) (1, 2) (c) (16, 6) (d) (3, 8)
  28. 28.What is the midpoint of the line joining (9, 9) and (15, 15)? (a) (12, 12) (b) (13, 12) (c) (24, 24) (d) (3, 3)
  29. 29.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 20 (c) 28 (d) 400
  30. 30.What is the midpoint of the line joining (0, 4) and (8, 14)? (a) (8, 18) (b) (4, 5) (c) (4, 9) (d) (9, 4)
  31. 31.What is the midpoint of the line joining (1, 10) and (7, 12)? (a) (3, 1) (b) (8, 22) (c) (11, 4) (d) (4, 11)
  32. 32.What is the distance between the points (2, 6) and (10, 12)? (a) 11 (b) 14 (c) 10 (d) 100
  33. 33.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 23 (c) 17 (d) 289
  34. 34.In which quadrant does the point (−7, −8) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  35. 35.What is the midpoint of the line joining (1, 14) and (7, 10)? (a) (12, 4) (b) (4, 12) (c) (8, 24) (d) (3, 2)
  36. 36.What is the distance between the points (2, 12) and (11, 0)? (a) 15 (b) 225 (c) 16 (d) 21
  37. 37.What is the distance between the points (7, 17) and (12, 5)? (a) 169 (b) 13 (c) 17 (d) 14
  38. 38.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 10 (c) 11 (d) 100
  39. 39.What is the distance between the points (2, 4) and (6, 7)? (a) 6 (b) 7 (c) 5 (d) 25
  40. 40.What is the midpoint of the line joining (7, 10) and (17, 14)? (a) (13, 12) (b) (5, 2) (c) (24, 24) (d) (12, 12)

Answer key

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

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