← Coordinates and distance lesson New set →

Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 538 · 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 (3, 4) and (7, 7)? (a) 6 (b) 7 (c) 25 (d) 5
  2. 2.What is the distance between the points (4, 0) and (20, 12)? (a) 400 (b) 21 (c) 20 (d) 28
  3. 3.What is the distance between the points (0, 16) and (12, 7)? (a) 21 (b) 225 (c) 15 (d) 16
  4. 4.In which quadrant does the point (−5, −7) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  5. 5.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 100 (c) 10 (d) 11
  6. 6.How far is the point (24, 7) from the origin (0, 0)? (a) 26 (b) 31 (c) 25 (d) 625
  7. 7.What is the distance between the points (9, 1) and (17, 16)? (a) 18 (b) 289 (c) 23 (d) 17
  8. 8.What is the midpoint of the line joining (1, 9) and (3, 13)? (a) (1, 2) (b) (2, 11) (c) (4, 22) (d) (11, 2)
  9. 9.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 6 (c) 7 (d) 5
  10. 10.In which quadrant does the point (−5, 7) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  11. 11.In which quadrant does the point (9, 3) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  12. 12.What is the midpoint of the line joining (2, 2) and (6, 12)? (a) (8, 14) (b) (7, 4) (c) (2, 5) (d) (4, 7)
  13. 13.What is the midpoint of the line joining (10, 9) and (16, 15)? (a) (3, 3) (b) (13, 12) (c) (26, 24) (d) (12, 13)
  14. 14.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 18 (c) 23 (d) 17
  15. 15.In which quadrant does the point (−3, 2) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  16. 16.What is the distance between the points (6, 11) and (9, 7)? (a) 7 (b) 5 (c) 6 (d) 25
  17. 17.What is the distance between the points (8, 0) and (32, 7)? (a) 25 (b) 625 (c) 26 (d) 31
  18. 18.In which quadrant does the point (−8, 7) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  19. 19.What is the midpoint of the line joining (8, 14) and (10, 10)? (a) (18, 24) (b) (12, 9) (c) (9, 12) (d) (1, 2)
  20. 20.In which quadrant does the point (−9, 5) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  21. 21.In which quadrant does the point (3, −7) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  22. 22.What is the distance between the points (5, 1) and (9, 4)? (a) 25 (b) 5 (c) 7 (d) 6
  23. 23.What is the distance between the points (6, 18) and (18, 2)? (a) 400 (b) 21 (c) 28 (d) 20
  24. 24.What is the distance between the points (1, 3) and (8, 27)? (a) 25 (b) 625 (c) 31 (d) 26
  25. 25.What is the midpoint of the line joining (1, 5) and (7, 7)? (a) (4, 6) (b) (6, 4) (c) (8, 12) (d) (3, 1)
  26. 26.What is the distance between the points (8, 4) and (20, 9)? (a) 13 (b) 14 (c) 169 (d) 17
  27. 27.In which quadrant does the point (−8, −1) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  28. 28.What is the distance between the points (4, 9) and (16, 25)? (a) 20 (b) 21 (c) 400 (d) 28
  29. 29.What is the distance between the points (9, 19) and (14, 7)? (a) 169 (b) 14 (c) 13 (d) 17
  30. 30.What is the midpoint of the line joining (7, 0) and (19, 4)? (a) (26, 4) (b) (6, 2) (c) (13, 2) (d) (2, 13)
  31. 31.What is the distance between the points (0, 19) and (5, 7)? (a) 14 (b) 13 (c) 17 (d) 169
  32. 32.What is the distance between the points (0, 1) and (3, 5)? (a) 7 (b) 25 (c) 6 (d) 5
  33. 33.What is the midpoint of the line joining (6, 8) and (12, 18)? (a) (3, 5) (b) (9, 13) (c) (18, 26) (d) (13, 9)
  34. 34.What is the distance between the points (0, 9) and (4, 12)? (a) 7 (b) 6 (c) 25 (d) 5
  35. 35.What is the distance between the points (6, 12) and (18, 7)? (a) 17 (b) 169 (c) 13 (d) 14
  36. 36.In which quadrant does the point (5, −1) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  37. 37.What is the midpoint of the line joining (1, 3) and (11, 11)? (a) (7, 6) (b) (5, 4) (c) (12, 14) (d) (6, 7)
  38. 38.What is the distance between the points (9, 0) and (21, 16)? (a) 28 (b) 20 (c) 400 (d) 21
  39. 39.In which quadrant does the point (1, 2) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  40. 40.What is the midpoint of the line joining (4, 16) and (16, 6)? (a) (10, 11) (b) (11, 10) (c) (6, 5) (d) (20, 22)

Answer key

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

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