← Coordinates and distance lesson New set →

Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 467 · 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 (5, −3) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  2. 2.What is the distance between the points (4, 7) and (13, 19)? (a) 21 (b) 15 (c) 16 (d) 225
  3. 3.What is the distance between the points (0, 4) and (3, 8)? (a) 7 (b) 25 (c) 5 (d) 6
  4. 4.What is the midpoint of the line joining (8, 18) and (10, 6)? (a) (1, 6) (b) (12, 9) (c) (18, 24) (d) (9, 12)
  5. 5.What is the midpoint of the line joining (5, 6) and (9, 0)? (a) (2, 3) (b) (14, 6) (c) (3, 7) (d) (7, 3)
  6. 6.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 625 (c) 25 (d) 31
  7. 7.In which quadrant does the point (−4, 9) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  8. 8.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 25 (c) 5 (d) 7
  9. 9.How far is the point (24, 7) from the origin (0, 0)? (a) 25 (b) 26 (c) 625 (d) 31
  10. 10.How far is the point (12, 9) from the origin (0, 0)? (a) 16 (b) 225 (c) 21 (d) 15
  11. 11.In which quadrant does the point (−7, 4) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  12. 12.What is the midpoint of the line joining (10, 20) and (14, 8)? (a) (24, 28) (b) (14, 12) (c) (2, 6) (d) (12, 14)
  13. 13.What is the midpoint of the line joining (6, 14) and (12, 8)? (a) (11, 9) (b) (3, 3) (c) (9, 11) (d) (18, 22)
  14. 14.What is the distance between the points (8, 19) and (13, 7)? (a) 14 (b) 13 (c) 17 (d) 169
  15. 15.What is the midpoint of the line joining (6, 5) and (10, 1)? (a) (8, 3) (b) (2, 2) (c) (16, 6) (d) (3, 8)
  16. 16.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 25 (c) 7 (d) 5
  17. 17.What is the distance between the points (7, 18) and (12, 6)? (a) 169 (b) 17 (c) 14 (d) 13
  18. 18.What is the distance between the points (8, 15) and (14, 7)? (a) 11 (b) 14 (c) 10 (d) 100
  19. 19.In which quadrant does the point (−5, 9) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  20. 20.What is the midpoint of the line joining (7, 2) and (13, 14)? (a) (3, 6) (b) (8, 10) (c) (20, 16) (d) (10, 8)
  21. 21.What is the midpoint of the line joining (9, 3) and (11, 7)? (a) (20, 10) (b) (5, 10) (c) (1, 2) (d) (10, 5)
  22. 22.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 400 (c) 21 (d) 20
  23. 23.What is the midpoint of the line joining (3, 14) and (13, 2)? (a) (16, 16) (b) (5, 6) (c) (8, 8) (d) (9, 8)
  24. 24.What is the distance between the points (8, 6) and (16, 21)? (a) 17 (b) 289 (c) 23 (d) 18
  25. 25.What is the distance between the points (8, 7) and (16, 1)? (a) 14 (b) 100 (c) 10 (d) 11
  26. 26.What is the distance between the points (6, 28) and (13, 4)? (a) 625 (b) 26 (c) 31 (d) 25
  27. 27.In which quadrant does the point (8, 7) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  28. 28.In which quadrant does the point (4, −5) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  29. 29.What is the midpoint of the line joining (2, 7) and (12, 1)? (a) (4, 7) (b) (7, 4) (c) (14, 8) (d) (5, 3)
  30. 30.In which quadrant does the point (7, 7) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  31. 31.What is the distance between the points (4, 13) and (9, 1)? (a) 169 (b) 14 (c) 13 (d) 17
  32. 32.What is the midpoint of the line joining (1, 3) and (3, 15)? (a) (4, 18) (b) (2, 9) (c) (9, 2) (d) (1, 6)
  33. 33.What is the distance between the points (8, 22) and (16, 7)? (a) 18 (b) 23 (c) 289 (d) 17
  34. 34.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 289 (c) 18 (d) 23
  35. 35.What is the distance between the points (3, 1) and (15, 17)? (a) 20 (b) 21 (c) 28 (d) 400
  36. 36.What is the distance between the points (4, 4) and (12, 19)? (a) 289 (b) 23 (c) 17 (d) 18
  37. 37.In which quadrant does the point (7, −2) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  38. 38.In which quadrant does the point (−3, 3) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  39. 39.What is the midpoint of the line joining (9, 8) and (17, 14)? (a) (4, 3) (b) (13, 11) (c) (11, 13) (d) (26, 22)
  40. 40.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 100 (c) 10 (d) 11

Answer key

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

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