← Coordinates and distance lesson New set →

Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 193 · 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 (8, 0) and (24, 12)? (a) 28 (b) 20 (c) 400 (d) 21
  2. 2.In which quadrant does the point (9, 9) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  3. 3.How far is the point (24, 7) from the origin (0, 0)? (a) 26 (b) 25 (c) 625 (d) 31
  4. 4.What is the distance between the points (4, 20) and (20, 8)? (a) 28 (b) 400 (c) 20 (d) 21
  5. 5.In which quadrant does the point (6, 2) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  6. 6.What is the distance between the points (7, 8) and (15, 2)? (a) 100 (b) 11 (c) 14 (d) 10
  7. 7.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 100 (c) 14 (d) 10
  8. 8.What is the distance between the points (0, 7) and (15, 15)? (a) 18 (b) 17 (c) 289 (d) 23
  9. 9.What is the midpoint of the line joining (10, 5) and (20, 13)? (a) (15, 9) (b) (30, 18) (c) (9, 15) (d) (5, 4)
  10. 10.In which quadrant does the point (−4, 5) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  11. 11.In which quadrant does the point (4, −3) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  12. 12.What is the distance between the points (4, 1) and (16, 17)? (a) 400 (b) 28 (c) 20 (d) 21
  13. 13.What is the distance between the points (5, 0) and (10, 12)? (a) 13 (b) 169 (c) 17 (d) 14
  14. 14.In which quadrant does the point (7, 5) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  15. 15.In which quadrant does the point (−9, −1) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  16. 16.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 17 (c) 23 (d) 289
  17. 17.What is the midpoint of the line joining (1, 6) and (13, 16)? (a) (6, 5) (b) (7, 11) (c) (14, 22) (d) (11, 7)
  18. 18.What is the distance between the points (3, 13) and (11, 7)? (a) 100 (b) 11 (c) 10 (d) 14
  19. 19.In which quadrant does the point (−6, 5) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  20. 20.What is the midpoint of the line joining (5, 0) and (17, 2)? (a) (6, 1) (b) (22, 2) (c) (1, 11) (d) (11, 1)
  21. 21.What is the distance between the points (8, 26) and (15, 2)? (a) 625 (b) 26 (c) 25 (d) 31
  22. 22.In which quadrant does the point (5, 8) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  23. 23.What is the midpoint of the line joining (3, 6) and (5, 4)? (a) (5, 4) (b) (1, 1) (c) (8, 10) (d) (4, 5)
  24. 24.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 13 (c) 14 (d) 17
  25. 25.What is the midpoint of the line joining (3, 10) and (5, 22)? (a) (16, 4) (b) (4, 16) (c) (1, 6) (d) (8, 32)
  26. 26.What is the distance between the points (2, 4) and (10, 19)? (a) 18 (b) 289 (c) 17 (d) 23
  27. 27.What is the midpoint of the line joining (0, 5) and (4, 3)? (a) (2, 4) (b) (2, 1) (c) (4, 8) (d) (4, 2)
  28. 28.In which quadrant does the point (−8, 7) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  29. 29.What is the distance between the points (6, 3) and (10, 6)? (a) 7 (b) 25 (c) 5 (d) 6
  30. 30.What is the midpoint of the line joining (6, 9) and (10, 5)? (a) (2, 2) (b) (8, 7) (c) (7, 8) (d) (16, 14)
  31. 31.What is the midpoint of the line joining (0, 1) and (6, 13)? (a) (3, 7) (b) (7, 3) (c) (6, 14) (d) (3, 6)
  32. 32.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 23 (c) 17 (d) 289
  33. 33.In which quadrant does the point (2, −7) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  34. 34.What is the distance between the points (5, 20) and (17, 4)? (a) 20 (b) 400 (c) 21 (d) 28
  35. 35.What is the distance between the points (0, 9) and (5, 21)? (a) 169 (b) 17 (c) 13 (d) 14
  36. 36.What is the midpoint of the line joining (3, 9) and (15, 15)? (a) (9, 12) (b) (6, 3) (c) (12, 9) (d) (18, 24)
  37. 37.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 25 (c) 5 (d) 7
  38. 38.What is the midpoint of the line joining (5, 3) and (15, 11)? (a) (20, 14) (b) (5, 4) (c) (10, 7) (d) (7, 10)
  39. 39.What is the distance between the points (7, 3) and (10, 7)? (a) 7 (b) 6 (c) 25 (d) 5
  40. 40.What is the distance between the points (2, 7) and (5, 3)? (a) 25 (b) 6 (c) 7 (d) 5

Answer key

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

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