← Coordinates and distance lesson New set →

Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 290 · 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 (4, −7) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  2. 2.In which quadrant does the point (−3, 5) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  3. 3.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 10 (c) 14 (d) 100
  4. 4.What is the distance between the points (0, 12) and (12, 3)? (a) 21 (b) 16 (c) 225 (d) 15
  5. 5.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 31 (c) 26 (d) 25
  6. 6.In which quadrant does the point (−4, 5) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  7. 7.What is the distance between the points (0, 3) and (8, 9)? (a) 10 (b) 14 (c) 11 (d) 100
  8. 8.In which quadrant does the point (4, 8) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  9. 9.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 289 (c) 18 (d) 23
  10. 10.What is the midpoint of the line joining (5, 5) and (9, 13)? (a) (7, 9) (b) (2, 4) (c) (9, 7) (d) (14, 18)
  11. 11.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 14 (c) 17 (d) 13
  12. 12.In which quadrant does the point (2, 9) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  13. 13.What is the distance between the points (6, 23) and (14, 8)? (a) 18 (b) 23 (c) 289 (d) 17
  14. 14.What is the distance between the points (6, 5) and (18, 21)? (a) 28 (b) 400 (c) 21 (d) 20
  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 (3, 0) and (10, 24)? (a) 31 (b) 625 (c) 26 (d) 25
  17. 17.What is the midpoint of the line joining (0, 16) and (12, 10)? (a) (12, 26) (b) (13, 6) (c) (6, 13) (d) (6, 3)
  18. 18.In which quadrant does the point (−7, 7) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  19. 19.What is the distance between the points (1, 6) and (6, 18)? (a) 17 (b) 14 (c) 169 (d) 13
  20. 20.What is the distance between the points (6, 17) and (21, 9)? (a) 23 (b) 289 (c) 17 (d) 18
  21. 21.In which quadrant does the point (−1, 3) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  22. 22.What is the distance between the points (1, 17) and (6, 5)? (a) 169 (b) 14 (c) 13 (d) 17
  23. 23.What is the distance between the points (9, 0) and (21, 9)? (a) 21 (b) 15 (c) 225 (d) 16
  24. 24.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 400 (c) 20 (d) 28
  25. 25.What is the distance between the points (4, 8) and (8, 11)? (a) 6 (b) 7 (c) 25 (d) 5
  26. 26.What is the distance between the points (6, 1) and (14, 7)? (a) 14 (b) 11 (c) 100 (d) 10
  27. 27.What is the midpoint of the line joining (4, 3) and (16, 15)? (a) (9, 10) (b) (10, 9) (c) (20, 18) (d) (6, 6)
  28. 28.What is the distance between the points (8, 5) and (24, 17)? (a) 21 (b) 28 (c) 20 (d) 400
  29. 29.What is the midpoint of the line joining (6, 10) and (16, 12)? (a) (11, 11) (b) (22, 22) (c) (5, 1) (d) (12, 11)
  30. 30.What is the distance between the points (6, 3) and (22, 15)? (a) 21 (b) 400 (c) 20 (d) 28
  31. 31.In which quadrant does the point (−6, −3) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  32. 32.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 17 (c) 13 (d) 14
  33. 33.What is the distance between the points (1, 4) and (25, 11)? (a) 625 (b) 26 (c) 25 (d) 31
  34. 34.What is the midpoint of the line joining (10, 17) and (12, 7)? (a) (11, 12) (b) (22, 24) (c) (12, 11) (d) (1, 5)
  35. 35.In which quadrant does the point (1, 9) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  36. 36.In which quadrant does the point (−8, −3) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  37. 37.What is the midpoint of the line joining (6, 0) and (10, 10)? (a) (2, 5) (b) (16, 10) (c) (8, 5) (d) (5, 8)
  38. 38.What is the midpoint of the line joining (8, 2) and (20, 4)? (a) (14, 3) (b) (3, 14) (c) (6, 1) (d) (28, 6)
  39. 39.What is the distance between the points (2, 5) and (10, 11)? (a) 10 (b) 100 (c) 14 (d) 11
  40. 40.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 5 (c) 7 (d) 6

Answer key

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

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