← Coordinates and distance lesson New set →

Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 163 · 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 distance between the points (3, 1) and (9, 9)? (a) 11 (b) 10 (c) 14 (d) 100
  2. 2.What is the distance between the points (4, 15) and (13, 3)? (a) 15 (b) 16 (c) 225 (d) 21
  3. 3.In which quadrant does the point (−5, −2) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  4. 4.What is the distance between the points (3, 6) and (15, 15)? (a) 15 (b) 16 (c) 21 (d) 225
  5. 5.How far is the point (24, 7) from the origin (0, 0)? (a) 25 (b) 26 (c) 31 (d) 625
  6. 6.In which quadrant does the point (−9, −8) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  7. 7.What is the midpoint of the line joining (3, 7) and (5, 15)? (a) (1, 4) (b) (8, 22) (c) (11, 4) (d) (4, 11)
  8. 8.In which quadrant does the point (−7, −4) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  9. 9.How far is the point (15, 8) from the origin (0, 0)? (a) 17 (b) 289 (c) 18 (d) 23
  10. 10.What is the midpoint of the line joining (5, 6) and (7, 14)? (a) (1, 4) (b) (10, 6) (c) (6, 10) (d) (12, 20)
  11. 11.What is the distance between the points (8, 2) and (17, 14)? (a) 21 (b) 15 (c) 225 (d) 16
  12. 12.What is the midpoint of the line joining (3, 15) and (7, 9)? (a) (2, 3) (b) (10, 24) (c) (12, 5) (d) (5, 12)
  13. 13.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 5 (c) 7 (d) 25
  14. 14.In which quadrant does the point (−6, 9) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  15. 15.What is the distance between the points (0, 16) and (16, 4)? (a) 20 (b) 400 (c) 28 (d) 21
  16. 16.What is the distance between the points (0, 0) and (8, 15)? (a) 23 (b) 17 (c) 18 (d) 289
  17. 17.In which quadrant does the point (9, −2) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  18. 18.In which quadrant does the point (7, 1) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  19. 19.What is the midpoint of the line joining (4, 7) and (10, 17)? (a) (14, 24) (b) (7, 12) (c) (3, 5) (d) (12, 7)
  20. 20.In which quadrant does the point (−4, 3) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  21. 21.What is the distance between the points (7, 12) and (31, 5)? (a) 31 (b) 25 (c) 26 (d) 625
  22. 22.What is the distance between the points (3, 33) and (10, 9)? (a) 625 (b) 31 (c) 25 (d) 26
  23. 23.What is the distance between the points (5, 9) and (9, 6)? (a) 5 (b) 25 (c) 7 (d) 6
  24. 24.What is the midpoint of the line joining (3, 9) and (5, 1)? (a) (1, 4) (b) (4, 5) (c) (5, 4) (d) (8, 10)
  25. 25.In which quadrant does the point (−3, −8) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  26. 26.How far is the point (7, 24) from the origin (0, 0)? (a) 25 (b) 31 (c) 26 (d) 625
  27. 27.In which quadrant does the point (3, −5) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  28. 28.In which quadrant does the point (9, −6) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  29. 29.What is the distance between the points (6, 0) and (12, 8)? (a) 14 (b) 11 (c) 100 (d) 10
  30. 30.What is the distance between the points (1, 17) and (10, 5)? (a) 21 (b) 225 (c) 15 (d) 16
  31. 31.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 11 (c) 14 (d) 100
  32. 32.What is the distance between the points (8, 20) and (16, 5)? (a) 18 (b) 289 (c) 23 (d) 17
  33. 33.What is the distance between the points (0, 1) and (3, 5)? (a) 6 (b) 7 (c) 5 (d) 25
  34. 34.What is the midpoint of the line joining (1, 10) and (5, 2)? (a) (6, 12) (b) (6, 3) (c) (2, 4) (d) (3, 6)
  35. 35.What is the midpoint of the line joining (0, 2) and (6, 0)? (a) (4, 1) (b) (3, 1) (c) (6, 2) (d) (1, 3)
  36. 36.What is the midpoint of the line joining (6, 2) and (14, 6)? (a) (4, 10) (b) (4, 2) (c) (20, 8) (d) (10, 4)
  37. 37.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 7 (c) 5 (d) 25
  38. 38.What is the midpoint of the line joining (3, 14) and (13, 8)? (a) (5, 3) (b) (11, 8) (c) (16, 22) (d) (8, 11)
  39. 39.In which quadrant does the point (7, −2) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  40. 40.What is the distance between the points (1, 1) and (13, 6)? (a) 14 (b) 169 (c) 13 (d) 17

Answer key

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

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