← Coordinates and distance lesson New set →

Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 55 · 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 (6, 1) and (10, 4)? (a) 6 (b) 7 (c) 25 (d) 5
  2. 2.In which quadrant does the point (−5, −5) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  3. 3.What is the midpoint of the line joining (9, 11) and (17, 1)? (a) (26, 12) (b) (13, 6) (c) (4, 5) (d) (6, 13)
  4. 4.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 16 (c) 15 (d) 21
  5. 5.What is the midpoint of the line joining (3, 12) and (15, 10)? (a) (11, 9) (b) (9, 11) (c) (6, 1) (d) (18, 22)
  6. 6.What is the distance between the points (0, 25) and (7, 1)? (a) 26 (b) 31 (c) 625 (d) 25
  7. 7.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 26 (c) 25 (d) 625
  8. 8.In which quadrant does the point (8, −1) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  9. 9.What is the midpoint of the line joining (8, 10) and (18, 12)? (a) (13, 11) (b) (11, 13) (c) (26, 22) (d) (5, 1)
  10. 10.What is the distance between the points (7, 1) and (15, 7)? (a) 100 (b) 10 (c) 14 (d) 11
  11. 11.What is the distance between the points (2, 18) and (14, 9)? (a) 15 (b) 21 (c) 225 (d) 16
  12. 12.What is the midpoint of the line joining (6, 2) and (8, 10)? (a) (6, 7) (b) (7, 6) (c) (1, 4) (d) (14, 12)
  13. 13.What is the midpoint of the line joining (1, 6) and (9, 14)? (a) (10, 5) (b) (4, 4) (c) (5, 10) (d) (10, 20)
  14. 14.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 6 (c) 7 (d) 5
  15. 15.In which quadrant does the point (3, −6) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  16. 16.What is the distance between the points (6, 33) and (13, 9)? (a) 26 (b) 625 (c) 25 (d) 31
  17. 17.What is the distance between the points (8, 24) and (15, 0)? (a) 31 (b) 25 (c) 625 (d) 26
  18. 18.In which quadrant does the point (−3, −6) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  19. 19.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 23 (c) 17 (d) 18
  20. 20.What is the distance between the points (7, 22) and (15, 7)? (a) 18 (b) 17 (c) 23 (d) 289
  21. 21.What is the distance between the points (0, 11) and (15, 3)? (a) 23 (b) 18 (c) 17 (d) 289
  22. 22.What is the midpoint of the line joining (1, 8) and (13, 18)? (a) (7, 13) (b) (14, 26) (c) (6, 5) (d) (13, 7)
  23. 23.What is the midpoint of the line joining (7, 5) and (9, 13)? (a) (1, 4) (b) (16, 18) (c) (9, 8) (d) (8, 9)
  24. 24.In which quadrant does the point (9, 5) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  25. 25.What is the distance between the points (5, 6) and (13, 0)? (a) 14 (b) 11 (c) 100 (d) 10
  26. 26.What is the midpoint of the line joining (9, 12) and (21, 8)? (a) (10, 15) (b) (15, 10) (c) (30, 20) (d) (6, 2)
  27. 27.In which quadrant does the point (−7, −9) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  28. 28.What is the midpoint of the line joining (8, 14) and (14, 2)? (a) (11, 8) (b) (3, 6) (c) (8, 11) (d) (22, 16)
  29. 29.What is the distance between the points (0, 1) and (3, 5)? (a) 25 (b) 6 (c) 7 (d) 5
  30. 30.What is the distance between the points (0, 5) and (9, 17)? (a) 21 (b) 225 (c) 16 (d) 15
  31. 31.What is the midpoint of the line joining (1, 4) and (13, 2)? (a) (6, 1) (b) (7, 3) (c) (14, 6) (d) (3, 7)
  32. 32.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 169 (c) 13 (d) 17
  33. 33.What is the distance between the points (1, 9) and (7, 17)? (a) 14 (b) 11 (c) 100 (d) 10
  34. 34.What is the distance between the points (4, 25) and (16, 9)? (a) 28 (b) 21 (c) 400 (d) 20
  35. 35.In which quadrant does the point (−7, 2) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  36. 36.In which quadrant does the point (−3, 6) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  37. 37.What is the distance between the points (4, 21) and (16, 5)? (a) 20 (b) 21 (c) 28 (d) 400
  38. 38.What is the distance between the points (2, 4) and (7, 16)? (a) 14 (b) 169 (c) 13 (d) 17
  39. 39.What is the midpoint of the line joining (6, 1) and (14, 11)? (a) (10, 6) (b) (4, 5) (c) (20, 12) (d) (6, 10)
  40. 40.In which quadrant does the point (−1, −8) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant

Answer key

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

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