← Coordinates and distance lesson New set →

Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 799 · 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 midpoint of the line joining (7, 6) and (13, 12)? (a) (10, 9) (b) (3, 3) (c) (9, 10) (d) (20, 18)
  2. 2.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 11 (c) 100 (d) 10
  3. 3.What is the distance between the points (7, 7) and (15, 22)? (a) 17 (b) 18 (c) 23 (d) 289
  4. 4.In which quadrant does the point (1, 2) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  5. 5.What is the distance between the points (2, 6) and (6, 3)? (a) 25 (b) 5 (c) 7 (d) 6
  6. 6.In which quadrant does the point (−6, 3) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  7. 7.In which quadrant does the point (−6, 7) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  8. 8.What is the distance between the points (7, 3) and (23, 15)? (a) 400 (b) 20 (c) 28 (d) 21
  9. 9.What is the distance between the points (7, 8) and (22, 0)? (a) 289 (b) 18 (c) 17 (d) 23
  10. 10.In which quadrant does the point (−3, −9) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  11. 11.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 20 (c) 400 (d) 21
  12. 12.What is the distance between the points (0, 8) and (6, 0)? (a) 100 (b) 11 (c) 14 (d) 10
  13. 13.What is the midpoint of the line joining (5, 10) and (13, 12)? (a) (4, 1) (b) (9, 11) (c) (18, 22) (d) (11, 9)
  14. 14.What is the distance between the points (0, 14) and (8, 8)? (a) 14 (b) 100 (c) 11 (d) 10
  15. 15.What is the distance between the points (8, 7) and (11, 11)? (a) 5 (b) 7 (c) 25 (d) 6
  16. 16.What is the distance between the points (0, 15) and (8, 9)? (a) 11 (b) 14 (c) 10 (d) 100
  17. 17.What is the distance between the points (1, 18) and (6, 6)? (a) 17 (b) 13 (c) 169 (d) 14
  18. 18.How far is the point (12, 9) from the origin (0, 0)? (a) 16 (b) 21 (c) 225 (d) 15
  19. 19.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 25 (c) 31 (d) 26
  20. 20.What is the midpoint of the line joining (10, 8) and (22, 14)? (a) (11, 16) (b) (6, 3) (c) (32, 22) (d) (16, 11)
  21. 21.What is the distance between the points (2, 7) and (11, 19)? (a) 15 (b) 225 (c) 16 (d) 21
  22. 22.In which quadrant does the point (−2, −8) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  23. 23.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 26 (c) 25 (d) 625
  24. 24.What is the distance between the points (6, 3) and (12, 11)? (a) 100 (b) 14 (c) 11 (d) 10
  25. 25.In which quadrant does the point (1, −4) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  26. 26.What is the midpoint of the line joining (7, 16) and (17, 6)? (a) (11, 12) (b) (24, 22) (c) (12, 11) (d) (5, 5)
  27. 27.What is the midpoint of the line joining (2, 1) and (8, 3)? (a) (2, 5) (b) (10, 4) (c) (3, 1) (d) (5, 2)
  28. 28.In which quadrant does the point (−1, −1) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  29. 29.What is the midpoint of the line joining (9, 5) and (15, 3)? (a) (4, 12) (b) (24, 8) (c) (12, 4) (d) (3, 1)
  30. 30.What is the midpoint of the line joining (3, 6) and (9, 2)? (a) (6, 4) (b) (12, 8) (c) (4, 6) (d) (3, 2)
  31. 31.What is the distance between the points (6, 4) and (10, 1)? (a) 6 (b) 25 (c) 7 (d) 5
  32. 32.What is the distance between the points (7, 2) and (22, 10)? (a) 23 (b) 18 (c) 289 (d) 17
  33. 33.In which quadrant does the point (2, 4) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  34. 34.What is the midpoint of the line joining (5, 9) and (11, 5)? (a) (7, 8) (b) (3, 2) (c) (16, 14) (d) (8, 7)
  35. 35.In which quadrant does the point (4, −6) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  36. 36.What is the midpoint of the line joining (8, 14) and (10, 6)? (a) (9, 10) (b) (10, 9) (c) (1, 4) (d) (18, 20)
  37. 37.What is the distance between the points (5, 7) and (17, 2)? (a) 13 (b) 14 (c) 169 (d) 17
  38. 38.What is the distance between the points (7, 15) and (31, 8)? (a) 26 (b) 625 (c) 25 (d) 31
  39. 39.What is the midpoint of the line joining (5, 10) and (15, 16)? (a) (20, 26) (b) (13, 10) (c) (10, 13) (d) (5, 3)
  40. 40.What is the midpoint of the line joining (2, 4) and (14, 8)? (a) (8, 6) (b) (6, 8) (c) (6, 2) (d) (16, 12)

Answer key

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

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