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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 856 · 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 (0, 3) and (6, 11)? (a) 100 (b) 14 (c) 11 (d) 10
  2. 2.What is the distance between the points (2, 9) and (14, 18)? (a) 15 (b) 21 (c) 225 (d) 16
  3. 3.In which quadrant does the point (−5, −2) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  4. 4.What is the distance between the points (5, 14) and (21, 2)? (a) 20 (b) 400 (c) 28 (d) 21
  5. 5.What is the distance between the points (7, 2) and (19, 11)? (a) 21 (b) 16 (c) 225 (d) 15
  6. 6.In which quadrant does the point (5, 4) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  7. 7.What is the midpoint of the line joining (3, 22) and (5, 10)? (a) (8, 32) (b) (16, 4) (c) (4, 16) (d) (1, 6)
  8. 8.In which quadrant does the point (−7, 6) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  9. 9.What is the distance between the points (7, 5) and (10, 1)? (a) 7 (b) 25 (c) 6 (d) 5
  10. 10.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 31 (c) 25 (d) 26
  11. 11.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 225 (c) 15 (d) 21
  12. 12.What is the distance between the points (1, 6) and (10, 18)? (a) 225 (b) 21 (c) 15 (d) 16
  13. 13.What is the distance between the points (9, 31) and (16, 7)? (a) 31 (b) 26 (c) 625 (d) 25
  14. 14.What is the midpoint of the line joining (10, 15) and (22, 5)? (a) (16, 10) (b) (32, 20) (c) (6, 5) (d) (10, 16)
  15. 15.What is the distance between the points (6, 25) and (13, 1)? (a) 625 (b) 25 (c) 26 (d) 31
  16. 16.What is the midpoint of the line joining (6, 8) and (8, 6)? (a) (14, 14) (b) (8, 7) (c) (7, 7) (d) (1, 1)
  17. 17.What is the midpoint of the line joining (8, 5) and (20, 15)? (a) (28, 20) (b) (6, 5) (c) (14, 10) (d) (10, 14)
  18. 18.What is the midpoint of the line joining (2, 11) and (4, 5)? (a) (6, 16) (b) (1, 3) (c) (3, 8) (d) (8, 3)
  19. 19.What is the midpoint of the line joining (0, 14) and (4, 6)? (a) (2, 10) (b) (2, 4) (c) (4, 20) (d) (10, 2)
  20. 20.In which quadrant does the point (−9, −2) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  21. 21.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 7 (c) 25 (d) 5
  22. 22.What is the distance between the points (0, 1) and (8, 7)? (a) 11 (b) 14 (c) 10 (d) 100
  23. 23.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 28 (c) 20 (d) 400
  24. 24.What is the distance between the points (6, 16) and (22, 4)? (a) 400 (b) 21 (c) 20 (d) 28
  25. 25.In which quadrant does the point (−1, 3) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  26. 26.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 11 (c) 10 (d) 100
  27. 27.What is the midpoint of the line joining (1, 18) and (13, 10)? (a) (7, 14) (b) (14, 28) (c) (6, 4) (d) (14, 7)
  28. 28.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 400 (c) 21 (d) 28
  29. 29.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 16 (c) 21 (d) 15
  30. 30.What is the distance between the points (1, 3) and (13, 12)? (a) 21 (b) 225 (c) 16 (d) 15
  31. 31.What is the distance between the points (4, 1) and (7, 5)? (a) 5 (b) 6 (c) 7 (d) 25
  32. 32.In which quadrant does the point (5, 9) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  33. 33.In which quadrant does the point (5, −7) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  34. 34.What is the distance between the points (7, 6) and (12, 18)? (a) 169 (b) 17 (c) 13 (d) 14
  35. 35.What is the distance between the points (3, 7) and (19, 19)? (a) 400 (b) 28 (c) 21 (d) 20
  36. 36.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 11 (c) 100 (d) 10
  37. 37.What is the midpoint of the line joining (8, 5) and (12, 11)? (a) (8, 10) (b) (10, 8) (c) (2, 3) (d) (20, 16)
  38. 38.In which quadrant does the point (−4, −3) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  39. 39.In which quadrant does the point (−2, −1) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  40. 40.What is the distance between the points (1, 27) and (8, 3)? (a) 25 (b) 625 (c) 26 (d) 31

Answer key

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

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