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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 866 · 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 (6, 8) from the origin (0, 0)? (a) 14 (b) 10 (c) 100 (d) 11
  2. 2.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 400 (c) 20 (d) 28
  3. 3.What is the midpoint of the line joining (10, 13) and (12, 1)? (a) (11, 7) (b) (1, 6) (c) (7, 11) (d) (22, 14)
  4. 4.What is the midpoint of the line joining (6, 7) and (14, 9)? (a) (8, 10) (b) (10, 8) (c) (4, 1) (d) (20, 16)
  5. 5.What is the midpoint of the line joining (4, 4) and (14, 2)? (a) (18, 6) (b) (3, 9) (c) (9, 3) (d) (5, 1)
  6. 6.What is the midpoint of the line joining (8, 8) and (16, 10)? (a) (4, 1) (b) (9, 12) (c) (24, 18) (d) (12, 9)
  7. 7.What is the distance between the points (0, 4) and (8, 19)? (a) 23 (b) 18 (c) 289 (d) 17
  8. 8.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 16 (c) 15 (d) 21
  9. 9.What is the midpoint of the line joining (3, 6) and (11, 12)? (a) (4, 3) (b) (9, 7) (c) (7, 9) (d) (14, 18)
  10. 10.What is the distance between the points (7, 7) and (16, 19)? (a) 15 (b) 16 (c) 225 (d) 21
  11. 11.In which quadrant does the point (−6, −1) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  12. 12.What is the distance between the points (7, 11) and (11, 8)? (a) 5 (b) 6 (c) 25 (d) 7
  13. 13.In which quadrant does the point (−1, 6) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  14. 14.What is the midpoint of the line joining (6, 6) and (12, 0)? (a) (9, 3) (b) (3, 3) (c) (3, 9) (d) (18, 6)
  15. 15.What is the distance between the points (1, 15) and (7, 7)? (a) 11 (b) 14 (c) 100 (d) 10
  16. 16.What is the distance between the points (0, 3) and (12, 8)? (a) 17 (b) 169 (c) 13 (d) 14
  17. 17.What is the midpoint of the line joining (9, 20) and (13, 8)? (a) (22, 28) (b) (11, 14) (c) (2, 6) (d) (14, 11)
  18. 18.What is the distance between the points (1, 18) and (10, 6)? (a) 21 (b) 15 (c) 225 (d) 16
  19. 19.What is the distance between the points (0, 11) and (12, 6)? (a) 17 (b) 169 (c) 14 (d) 13
  20. 20.What is the midpoint of the line joining (6, 0) and (8, 12)? (a) (14, 12) (b) (7, 6) (c) (6, 7) (d) (1, 6)
  21. 21.What is the distance between the points (1, 2) and (5, 5)? (a) 25 (b) 5 (c) 6 (d) 7
  22. 22.What is the midpoint of the line joining (4, 9) and (16, 7)? (a) (20, 16) (b) (8, 10) (c) (6, 1) (d) (10, 8)
  23. 23.What is the midpoint of the line joining (1, 8) and (9, 12)? (a) (10, 5) (b) (4, 2) (c) (10, 20) (d) (5, 10)
  24. 24.What is the distance between the points (1, 5) and (13, 21)? (a) 400 (b) 28 (c) 21 (d) 20
  25. 25.How far is the point (12, 5) from the origin (0, 0)? (a) 13 (b) 14 (c) 17 (d) 169
  26. 26.What is the distance between the points (1, 1) and (6, 13)? (a) 13 (b) 169 (c) 14 (d) 17
  27. 27.In which quadrant does the point (−2, −2) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  28. 28.What is the midpoint of the line joining (2, 3) and (6, 5)? (a) (8, 8) (b) (5, 4) (c) (4, 4) (d) (2, 1)
  29. 29.What is the midpoint of the line joining (10, 9) and (20, 17)? (a) (15, 13) (b) (30, 26) (c) (13, 15) (d) (5, 4)
  30. 30.In which quadrant does the point (2, −4) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  31. 31.What is the distance between the points (5, 16) and (13, 1)? (a) 289 (b) 23 (c) 18 (d) 17
  32. 32.In which quadrant does the point (−7, −7) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  33. 33.What is the distance between the points (1, 4) and (9, 19)? (a) 289 (b) 23 (c) 17 (d) 18
  34. 34.What is the distance between the points (5, 0) and (12, 24)? (a) 625 (b) 25 (c) 26 (d) 31
  35. 35.In which quadrant does the point (−3, −7) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  36. 36.What is the distance between the points (6, 13) and (14, 7)? (a) 14 (b) 11 (c) 100 (d) 10
  37. 37.What is the distance between the points (3, 14) and (27, 7)? (a) 31 (b) 625 (c) 26 (d) 25
  38. 38.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 5 (c) 25 (d) 6
  39. 39.What is the distance between the points (4, 5) and (16, 14)? (a) 15 (b) 225 (c) 16 (d) 21
  40. 40.What is the distance between the points (2, 8) and (6, 11)? (a) 7 (b) 6 (c) 5 (d) 25

Answer key

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

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