← Coordinates and distance lesson New set →

Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 288 · 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 (4, 18) and (20, 6)? (a) 20 (b) 400 (c) 28 (d) 21
  2. 2.What is the midpoint of the line joining (3, 18) and (15, 10)? (a) (9, 14) (b) (14, 9) (c) (18, 28) (d) (6, 4)
  3. 3.In which quadrant does the point (−9, 1) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  4. 4.In which quadrant does the point (5, 7) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  5. 5.What is the midpoint of the line joining (8, 12) and (12, 8)? (a) (2, 2) (b) (11, 10) (c) (20, 20) (d) (10, 10)
  6. 6.What is the midpoint of the line joining (10, 0) and (22, 12)? (a) (32, 12) (b) (6, 6) (c) (16, 6) (d) (6, 16)
  7. 7.What is the midpoint of the line joining (0, 6) and (4, 4)? (a) (2, 1) (b) (2, 5) (c) (4, 10) (d) (5, 2)
  8. 8.How far is the point (12, 9) from the origin (0, 0)? (a) 16 (b) 21 (c) 225 (d) 15
  9. 9.What is the distance between the points (7, 4) and (10, 8)? (a) 6 (b) 7 (c) 25 (d) 5
  10. 10.In which quadrant does the point (5, −1) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  11. 11.What is the distance between the points (5, 17) and (21, 5)? (a) 20 (b) 400 (c) 28 (d) 21
  12. 12.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 26 (c) 25 (d) 625
  13. 13.In which quadrant does the point (7, 1) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  14. 14.In which quadrant does the point (1, 2) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  15. 15.What is the distance between the points (1, 7) and (4, 3)? (a) 5 (b) 25 (c) 6 (d) 7
  16. 16.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 13 (c) 17 (d) 169
  17. 17.What is the distance between the points (7, 12) and (23, 0)? (a) 20 (b) 400 (c) 21 (d) 28
  18. 18.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 14 (c) 11 (d) 10
  19. 19.What is the midpoint of the line joining (4, 8) and (8, 4)? (a) (12, 12) (b) (6, 6) (c) (2, 2) (d) (7, 6)
  20. 20.What is the distance between the points (0, 5) and (9, 17)? (a) 225 (b) 21 (c) 16 (d) 15
  21. 21.What is the distance between the points (2, 22) and (14, 6)? (a) 28 (b) 21 (c) 20 (d) 400
  22. 22.What is the midpoint of the line joining (7, 11) and (19, 9)? (a) (10, 13) (b) (13, 10) (c) (26, 20) (d) (6, 1)
  23. 23.What is the distance between the points (8, 8) and (20, 13)? (a) 13 (b) 17 (c) 169 (d) 14
  24. 24.In which quadrant does the point (6, 4) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  25. 25.In which quadrant does the point (6, 1) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  26. 26.What is the distance between the points (6, 2) and (11, 14)? (a) 13 (b) 14 (c) 17 (d) 169
  27. 27.What is the midpoint of the line joining (1, 10) and (5, 18)? (a) (3, 14) (b) (6, 28) (c) (14, 3) (d) (2, 4)
  28. 28.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 6 (c) 5 (d) 7
  29. 29.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 10 (c) 14 (d) 11
  30. 30.What is the distance between the points (2, 26) and (9, 2)? (a) 25 (b) 625 (c) 31 (d) 26
  31. 31.What is the midpoint of the line joining (10, 5) and (20, 1)? (a) (15, 3) (b) (5, 2) (c) (3, 15) (d) (30, 6)
  32. 32.What is the midpoint of the line joining (4, 7) and (6, 11)? (a) (9, 5) (b) (1, 2) (c) (5, 9) (d) (10, 18)
  33. 33.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 25 (c) 625 (d) 26
  34. 34.What is the distance between the points (7, 0) and (12, 12)? (a) 13 (b) 14 (c) 169 (d) 17
  35. 35.What is the distance between the points (9, 2) and (21, 18)? (a) 28 (b) 400 (c) 20 (d) 21
  36. 36.What is the distance between the points (5, 4) and (13, 10)? (a) 14 (b) 100 (c) 10 (d) 11
  37. 37.In which quadrant does the point (4, 5) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  38. 38.What is the distance between the points (0, 2) and (9, 14)? (a) 16 (b) 15 (c) 21 (d) 225
  39. 39.What is the midpoint of the line joining (3, 0) and (11, 10)? (a) (5, 7) (b) (4, 5) (c) (14, 10) (d) (7, 5)
  40. 40.In which quadrant does the point (3, 9) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant

Answer key

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

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