← Coordinates and distance lesson New set →

Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 628 · 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 (1, −8) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  2. 2.What is the distance between the points (8, 0) and (32, 7)? (a) 26 (b) 625 (c) 25 (d) 31
  3. 3.In which quadrant does the point (7, 3) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  4. 4.What is the distance between the points (4, 6) and (9, 18)? (a) 169 (b) 14 (c) 17 (d) 13
  5. 5.In which quadrant does the point (9, −1) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  6. 6.What is the midpoint of the line joining (10, 0) and (16, 8)? (a) (4, 13) (b) (13, 4) (c) (26, 8) (d) (3, 4)
  7. 7.What is the distance between the points (2, 7) and (5, 11)? (a) 7 (b) 25 (c) 5 (d) 6
  8. 8.What is the distance between the points (9, 0) and (14, 12)? (a) 14 (b) 169 (c) 17 (d) 13
  9. 9.What is the midpoint of the line joining (2, 22) and (14, 10)? (a) (16, 32) (b) (6, 6) (c) (16, 8) (d) (8, 16)
  10. 10.What is the midpoint of the line joining (9, 1) and (11, 7)? (a) (20, 8) (b) (4, 10) (c) (10, 4) (d) (1, 3)
  11. 11.What is the distance between the points (5, 7) and (17, 16)? (a) 21 (b) 15 (c) 225 (d) 16
  12. 12.What is the midpoint of the line joining (0, 7) and (2, 19)? (a) (2, 26) (b) (13, 1) (c) (1, 6) (d) (1, 13)
  13. 13.In which quadrant does the point (−8, 6) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  14. 14.What is the midpoint of the line joining (6, 19) and (8, 7)? (a) (13, 7) (b) (7, 13) (c) (14, 26) (d) (1, 6)
  15. 15.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 225 (c) 16 (d) 15
  16. 16.What is the distance between the points (4, 2) and (10, 10)? (a) 10 (b) 14 (c) 11 (d) 100
  17. 17.What is the distance between the points (2, 1) and (6, 4)? (a) 7 (b) 5 (c) 25 (d) 6
  18. 18.What is the distance between the points (1, 6) and (25, 13)? (a) 625 (b) 31 (c) 25 (d) 26
  19. 19.What is the distance between the points (6, 14) and (22, 2)? (a) 21 (b) 28 (c) 20 (d) 400
  20. 20.What is the distance between the points (8, 0) and (16, 6)? (a) 11 (b) 14 (c) 10 (d) 100
  21. 21.What is the midpoint of the line joining (8, 16) and (12, 8)? (a) (10, 12) (b) (2, 4) (c) (12, 10) (d) (20, 24)
  22. 22.What is the distance between the points (3, 4) and (7, 7)? (a) 6 (b) 5 (c) 7 (d) 25
  23. 23.What is the distance between the points (8, 2) and (20, 11)? (a) 21 (b) 16 (c) 225 (d) 15
  24. 24.What is the distance between the points (1, 1) and (9, 7)? (a) 11 (b) 14 (c) 10 (d) 100
  25. 25.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 169 (c) 13 (d) 17
  26. 26.What is the midpoint of the line joining (3, 5) and (7, 1)? (a) (2, 2) (b) (5, 3) (c) (3, 5) (d) (10, 6)
  27. 27.What is the midpoint of the line joining (7, 6) and (13, 8)? (a) (20, 14) (b) (3, 1) (c) (7, 10) (d) (10, 7)
  28. 28.What is the midpoint of the line joining (5, 6) and (9, 10)? (a) (7, 8) (b) (8, 7) (c) (14, 16) (d) (2, 2)
  29. 29.What is the distance between the points (6, 33) and (13, 9)? (a) 26 (b) 31 (c) 25 (d) 625
  30. 30.What is the distance between the points (8, 28) and (15, 4)? (a) 25 (b) 31 (c) 26 (d) 625
  31. 31.What is the midpoint of the line joining (5, 6) and (17, 4)? (a) (22, 10) (b) (6, 1) (c) (11, 5) (d) (5, 11)
  32. 32.What is the distance between the points (1, 14) and (6, 2)? (a) 13 (b) 169 (c) 17 (d) 14
  33. 33.What is the midpoint of the line joining (0, 5) and (2, 9)? (a) (1, 2) (b) (7, 1) (c) (1, 7) (d) (2, 14)
  34. 34.In which quadrant does the point (1, 1) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  35. 35.What is the midpoint of the line joining (4, 12) and (10, 4)? (a) (3, 4) (b) (7, 8) (c) (14, 16) (d) (8, 7)
  36. 36.What is the distance between the points (3, 5) and (9, 13)? (a) 10 (b) 11 (c) 14 (d) 100
  37. 37.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 28 (c) 400 (d) 20
  38. 38.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 15 (c) 225 (d) 16
  39. 39.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 23 (c) 289 (d) 17
  40. 40.What is the midpoint of the line joining (4, 9) and (14, 13)? (a) (9, 11) (b) (18, 22) (c) (11, 9) (d) (5, 2)

Answer key

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

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