← Coordinates and distance lesson New set →

Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 683 · 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.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 20 (c) 28 (d) 400
  2. 2.What is the distance between the points (7, 24) and (15, 9)? (a) 18 (b) 289 (c) 23 (d) 17
  3. 3.What is the distance between the points (6, 2) and (12, 10)? (a) 100 (b) 11 (c) 14 (d) 10
  4. 4.What is the midpoint of the line joining (0, 19) and (10, 9)? (a) (14, 5) (b) (5, 5) (c) (5, 14) (d) (10, 28)
  5. 5.What is the midpoint of the line joining (1, 8) and (13, 4)? (a) (14, 12) (b) (6, 7) (c) (7, 6) (d) (6, 2)
  6. 6.In which quadrant does the point (9, −8) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  7. 7.What is the midpoint of the line joining (10, 16) and (18, 8)? (a) (14, 12) (b) (28, 24) (c) (12, 14) (d) (4, 4)
  8. 8.What is the midpoint of the line joining (9, 0) and (19, 10)? (a) (28, 10) (b) (5, 5) (c) (5, 14) (d) (14, 5)
  9. 9.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 289 (c) 17 (d) 23
  10. 10.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 31 (c) 26 (d) 25
  11. 11.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 5 (c) 6 (d) 25
  12. 12.In which quadrant does the point (−6, 7) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  13. 13.What is the distance between the points (1, 15) and (9, 0)? (a) 18 (b) 17 (c) 23 (d) 289
  14. 14.What is the distance between the points (0, 7) and (7, 31)? (a) 31 (b) 25 (c) 625 (d) 26
  15. 15.What is the midpoint of the line joining (2, 12) and (10, 4)? (a) (6, 8) (b) (4, 4) (c) (8, 6) (d) (12, 16)
  16. 16.What is the distance between the points (0, 2) and (12, 7)? (a) 169 (b) 14 (c) 17 (d) 13
  17. 17.What is the distance between the points (2, 8) and (14, 24)? (a) 400 (b) 28 (c) 21 (d) 20
  18. 18.What is the midpoint of the line joining (10, 6) and (20, 10)? (a) (8, 15) (b) (30, 16) (c) (15, 8) (d) (5, 2)
  19. 19.In which quadrant does the point (6, −1) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  20. 20.What is the distance between the points (9, 14) and (15, 6)? (a) 14 (b) 11 (c) 100 (d) 10
  21. 21.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 225 (c) 15 (d) 16
  22. 22.What is the midpoint of the line joining (1, 0) and (13, 12)? (a) (6, 6) (b) (6, 7) (c) (14, 12) (d) (7, 6)
  23. 23.What is the midpoint of the line joining (6, 9) and (16, 7)? (a) (22, 16) (b) (8, 11) (c) (11, 8) (d) (5, 1)
  24. 24.What is the midpoint of the line joining (10, 4) and (12, 0)? (a) (11, 2) (b) (22, 4) (c) (2, 11) (d) (1, 2)
  25. 25.What is the midpoint of the line joining (0, 9) and (8, 13)? (a) (4, 2) (b) (4, 11) (c) (11, 4) (d) (8, 22)
  26. 26.What is the midpoint of the line joining (4, 5) and (6, 9)? (a) (1, 2) (b) (10, 14) (c) (7, 5) (d) (5, 7)
  27. 27.What is the distance between the points (1, 9) and (9, 15)? (a) 11 (b) 10 (c) 14 (d) 100
  28. 28.In which quadrant does the point (1, −2) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  29. 29.What is the distance between the points (8, 15) and (14, 7)? (a) 11 (b) 100 (c) 14 (d) 10
  30. 30.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 10 (c) 14 (d) 100
  31. 31.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 17 (c) 14 (d) 13
  32. 32.In which quadrant does the point (−2, −5) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  33. 33.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 15 (c) 16 (d) 225
  34. 34.What is the midpoint of the line joining (8, 18) and (12, 6)? (a) (20, 24) (b) (2, 6) (c) (12, 10) (d) (10, 12)
  35. 35.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 5 (c) 7 (d) 25
  36. 36.What is the distance between the points (5, 9) and (10, 21)? (a) 14 (b) 169 (c) 13 (d) 17
  37. 37.What is the distance between the points (0, 32) and (7, 8)? (a) 625 (b) 31 (c) 26 (d) 25
  38. 38.In which quadrant does the point (−3, 1) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  39. 39.What is the distance between the points (2, 16) and (10, 1)? (a) 23 (b) 289 (c) 17 (d) 18
  40. 40.What is the midpoint of the line joining (5, 2) and (7, 4)? (a) (1, 1) (b) (12, 6) (c) (6, 3) (d) (3, 6)

Answer key

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

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