← Coordinates and distance lesson New set →

Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 607 · 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 (−6, −1) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  2. 2.In which quadrant does the point (5, 6) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  3. 3.What is the distance between the points (1, 13) and (25, 6)? (a) 26 (b) 25 (c) 625 (d) 31
  4. 4.What is the midpoint of the line joining (9, 4) and (19, 10)? (a) (7, 14) (b) (14, 7) (c) (28, 14) (d) (5, 3)
  5. 5.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 21 (c) 15 (d) 16
  6. 6.What is the distance between the points (8, 1) and (12, 4)? (a) 25 (b) 7 (c) 6 (d) 5
  7. 7.What is the distance between the points (3, 12) and (8, 0)? (a) 169 (b) 14 (c) 13 (d) 17
  8. 8.What is the distance between the points (2, 1) and (14, 17)? (a) 28 (b) 20 (c) 21 (d) 400
  9. 9.What is the midpoint of the line joining (3, 4) and (5, 8)? (a) (6, 4) (b) (8, 12) (c) (1, 2) (d) (4, 6)
  10. 10.What is the distance between the points (5, 13) and (20, 5)? (a) 289 (b) 17 (c) 18 (d) 23
  11. 11.What is the distance between the points (3, 15) and (27, 8)? (a) 26 (b) 25 (c) 625 (d) 31
  12. 12.In which quadrant does the point (−3, −1) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  13. 13.What is the midpoint of the line joining (10, 2) and (22, 12)? (a) (7, 16) (b) (16, 7) (c) (32, 14) (d) (6, 5)
  14. 14.In which quadrant does the point (5, −1) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  15. 15.In which quadrant does the point (8, −2) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  16. 16.How far is the point (7, 24) from the origin (0, 0)? (a) 25 (b) 31 (c) 625 (d) 26
  17. 17.In which quadrant does the point (2, 2) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  18. 18.How far is the point (12, 5) from the origin (0, 0)? (a) 13 (b) 17 (c) 14 (d) 169
  19. 19.What is the midpoint of the line joining (9, 11) and (15, 5)? (a) (24, 16) (b) (12, 8) (c) (3, 3) (d) (8, 12)
  20. 20.What is the midpoint of the line joining (2, 16) and (12, 8)? (a) (12, 7) (b) (5, 4) (c) (14, 24) (d) (7, 12)
  21. 21.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 21 (c) 20 (d) 400
  22. 22.What is the distance between the points (9, 16) and (25, 4)? (a) 20 (b) 21 (c) 400 (d) 28
  23. 23.In which quadrant does the point (−9, −3) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  24. 24.What is the distance between the points (6, 12) and (9, 8)? (a) 6 (b) 5 (c) 7 (d) 25
  25. 25.In which quadrant does the point (−1, −2) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  26. 26.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 11 (c) 14 (d) 100
  27. 27.What is the midpoint of the line joining (5, 18) and (7, 8)? (a) (13, 6) (b) (12, 26) (c) (6, 13) (d) (1, 5)
  28. 28.What is the distance between the points (7, 4) and (14, 28)? (a) 25 (b) 31 (c) 625 (d) 26
  29. 29.What is the midpoint of the line joining (9, 2) and (15, 10)? (a) (24, 12) (b) (6, 12) (c) (12, 6) (d) (3, 4)
  30. 30.What is the distance between the points (2, 7) and (14, 2)? (a) 17 (b) 13 (c) 169 (d) 14
  31. 31.In which quadrant does the point (−2, 7) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  32. 32.What is the distance between the points (2, 9) and (6, 12)? (a) 5 (b) 25 (c) 7 (d) 6
  33. 33.What is the distance between the points (4, 16) and (16, 0)? (a) 28 (b) 21 (c) 400 (d) 20
  34. 34.What is the midpoint of the line joining (6, 10) and (10, 22)? (a) (2, 6) (b) (16, 32) (c) (8, 16) (d) (16, 8)
  35. 35.What is the distance between the points (3, 18) and (11, 3)? (a) 23 (b) 18 (c) 17 (d) 289
  36. 36.What is the distance between the points (5, 9) and (17, 14)? (a) 169 (b) 14 (c) 17 (d) 13
  37. 37.What is the distance between the points (3, 8) and (11, 14)? (a) 11 (b) 100 (c) 14 (d) 10
  38. 38.What is the distance between the points (8, 7) and (11, 11)? (a) 25 (b) 7 (c) 6 (d) 5
  39. 39.What is the distance between the points (6, 12) and (30, 5)? (a) 26 (b) 31 (c) 25 (d) 625
  40. 40.What is the distance between the points (5, 4) and (14, 16)? (a) 225 (b) 16 (c) 21 (d) 15

Answer key

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

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