← Coordinates and distance lesson New set →

Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 569 · 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, 5) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  2. 2.In which quadrant does the point (−9, −7) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  3. 3.What is the distance between the points (6, 4) and (18, 20)? (a) 400 (b) 20 (c) 21 (d) 28
  4. 4.What is the distance between the points (1, 7) and (8, 31)? (a) 26 (b) 31 (c) 625 (d) 25
  5. 5.What is the distance between the points (2, 20) and (10, 5)? (a) 23 (b) 289 (c) 18 (d) 17
  6. 6.What is the midpoint of the line joining (9, 9) and (21, 21)? (a) (6, 6) (b) (15, 15) (c) (30, 30) (d) (16, 15)
  7. 7.In which quadrant does the point (−2, 7) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  8. 8.What is the midpoint of the line joining (4, 10) and (12, 4)? (a) (16, 14) (b) (8, 7) (c) (4, 3) (d) (7, 8)
  9. 9.In which quadrant does the point (1, −4) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  10. 10.What is the midpoint of the line joining (4, 8) and (8, 2)? (a) (5, 6) (b) (12, 10) (c) (2, 3) (d) (6, 5)
  11. 11.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 400 (c) 21 (d) 20
  12. 12.What is the distance between the points (5, 19) and (13, 4)? (a) 17 (b) 289 (c) 23 (d) 18
  13. 13.What is the distance between the points (8, 6) and (20, 1)? (a) 14 (b) 17 (c) 13 (d) 169
  14. 14.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 26 (c) 625 (d) 25
  15. 15.What is the midpoint of the line joining (0, 15) and (8, 7)? (a) (4, 4) (b) (11, 4) (c) (8, 22) (d) (4, 11)
  16. 16.In which quadrant does the point (3, −9) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  17. 17.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 5 (c) 7 (d) 25
  18. 18.In which quadrant does the point (−1, −6) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  19. 19.What is the midpoint of the line joining (7, 12) and (19, 2)? (a) (6, 5) (b) (26, 14) (c) (7, 13) (d) (13, 7)
  20. 20.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 23 (c) 18 (d) 17
  21. 21.What is the distance between the points (0, 4) and (4, 1)? (a) 6 (b) 25 (c) 7 (d) 5
  22. 22.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 17 (c) 14 (d) 13
  23. 23.What is the midpoint of the line joining (4, 0) and (16, 2)? (a) (1, 10) (b) (6, 1) (c) (20, 2) (d) (10, 1)
  24. 24.What is the midpoint of the line joining (3, 3) and (5, 11)? (a) (8, 14) (b) (1, 4) (c) (4, 7) (d) (7, 4)
  25. 25.What is the midpoint of the line joining (8, 10) and (12, 22)? (a) (16, 10) (b) (2, 6) (c) (20, 32) (d) (10, 16)
  26. 26.What is the midpoint of the line joining (8, 7) and (10, 11)? (a) (10, 9) (b) (1, 2) (c) (9, 9) (d) (18, 18)
  27. 27.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 31 (c) 26 (d) 25
  28. 28.What is the midpoint of the line joining (3, 3) and (9, 15)? (a) (12, 18) (b) (6, 9) (c) (3, 6) (d) (9, 6)
  29. 29.What is the distance between the points (2, 16) and (26, 9)? (a) 26 (b) 31 (c) 25 (d) 625
  30. 30.In which quadrant does the point (−4, 3) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  31. 31.What is the distance between the points (9, 7) and (33, 0)? (a) 26 (b) 625 (c) 25 (d) 31
  32. 32.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 17 (c) 289 (d) 23
  33. 33.What is the midpoint of the line joining (6, 5) and (16, 15)? (a) (11, 10) (b) (5, 5) (c) (10, 11) (d) (22, 20)
  34. 34.What is the distance between the points (9, 18) and (17, 3)? (a) 18 (b) 17 (c) 289 (d) 23
  35. 35.In which quadrant does the point (−1, −3) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  36. 36.How far is the point (12, 16) from the origin (0, 0)? (a) 20 (b) 21 (c) 28 (d) 400
  37. 37.What is the midpoint of the line joining (1, 9) and (11, 5)? (a) (5, 2) (b) (12, 14) (c) (6, 7) (d) (7, 6)
  38. 38.In which quadrant does the point (1, −7) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  39. 39.What is the distance between the points (5, 4) and (14, 16)? (a) 225 (b) 21 (c) 16 (d) 15
  40. 40.What is the distance between the points (9, 2) and (21, 11)? (a) 21 (b) 16 (c) 15 (d) 225

Answer key

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

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