← Coordinates and distance lesson New set →

Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 846 · 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.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 25 (c) 31 (d) 26
  2. 2.What is the midpoint of the line joining (1, 10) and (13, 12)? (a) (11, 7) (b) (7, 11) (c) (6, 1) (d) (14, 22)
  3. 3.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 17 (c) 13 (d) 14
  4. 4.What is the distance between the points (9, 6) and (21, 11)? (a) 169 (b) 13 (c) 14 (d) 17
  5. 5.In which quadrant does the point (7, 6) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  6. 6.In which quadrant does the point (4, 2) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  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 midpoint of the line joining (4, 16) and (16, 6)? (a) (20, 22) (b) (10, 11) (c) (11, 10) (d) (6, 5)
  9. 9.In which quadrant does the point (−8, −7) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  10. 10.How far is the point (24, 7) from the origin (0, 0)? (a) 26 (b) 31 (c) 25 (d) 625
  11. 11.What is the distance between the points (3, 5) and (15, 21)? (a) 21 (b) 20 (c) 400 (d) 28
  12. 12.In which quadrant does the point (2, −3) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  13. 13.What is the midpoint of the line joining (10, 7) and (12, 19)? (a) (22, 26) (b) (11, 13) (c) (13, 11) (d) (1, 6)
  14. 14.What is the midpoint of the line joining (8, 15) and (10, 5)? (a) (10, 9) (b) (1, 5) (c) (9, 10) (d) (18, 20)
  15. 15.What is the distance between the points (4, 12) and (16, 3)? (a) 15 (b) 21 (c) 225 (d) 16
  16. 16.What is the distance between the points (2, 0) and (11, 12)? (a) 225 (b) 21 (c) 16 (d) 15
  17. 17.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 23 (c) 18 (d) 17
  18. 18.What is the midpoint of the line joining (1, 4) and (3, 10)? (a) (2, 7) (b) (4, 14) (c) (1, 3) (d) (7, 2)
  19. 19.What is the distance between the points (0, 4) and (12, 13)? (a) 21 (b) 225 (c) 15 (d) 16
  20. 20.What is the distance between the points (7, 0) and (23, 12)? (a) 28 (b) 20 (c) 400 (d) 21
  21. 21.What is the midpoint of the line joining (0, 9) and (8, 11)? (a) (8, 20) (b) (10, 4) (c) (4, 1) (d) (4, 10)
  22. 22.In which quadrant does the point (2, 2) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  23. 23.What is the distance between the points (9, 11) and (21, 2)? (a) 15 (b) 16 (c) 225 (d) 21
  24. 24.In which quadrant does the point (−2, 3) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  25. 25.In which quadrant does the point (−5, 6) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  26. 26.What is the midpoint of the line joining (1, 3) and (7, 15)? (a) (3, 6) (b) (9, 4) (c) (8, 18) (d) (4, 9)
  27. 27.What is the distance between the points (6, 10) and (30, 3)? (a) 625 (b) 25 (c) 26 (d) 31
  28. 28.In which quadrant does the point (9, −5) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  29. 29.What is the distance between the points (7, 6) and (12, 18)? (a) 13 (b) 17 (c) 169 (d) 14
  30. 30.What is the midpoint of the line joining (0, 7) and (10, 9)? (a) (10, 16) (b) (8, 5) (c) (5, 8) (d) (5, 1)
  31. 31.How far is the point (12, 9) from the origin (0, 0)? (a) 15 (b) 21 (c) 225 (d) 16
  32. 32.What is the midpoint of the line joining (6, 2) and (10, 8)? (a) (2, 3) (b) (5, 8) (c) (16, 10) (d) (8, 5)
  33. 33.In which quadrant does the point (1, 3) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  34. 34.In which quadrant does the point (−1, −6) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  35. 35.In which quadrant does the point (−5, −1) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  36. 36.What is the midpoint of the line joining (3, 6) and (7, 10)? (a) (8, 5) (b) (2, 2) (c) (10, 16) (d) (5, 8)
  37. 37.What is the midpoint of the line joining (7, 7) and (11, 11)? (a) (10, 9) (b) (18, 18) (c) (2, 2) (d) (9, 9)
  38. 38.In which quadrant does the point (4, 9) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  39. 39.What is the midpoint of the line joining (1, 4) and (3, 12)? (a) (2, 8) (b) (1, 4) (c) (4, 16) (d) (8, 2)
  40. 40.What is the distance between the points (0, 15) and (8, 0)? (a) 23 (b) 17 (c) 289 (d) 18

Answer key

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

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