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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 313 · 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 (−2, 9) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  2. 2.What is the midpoint of the line joining (4, 4) and (16, 12)? (a) (10, 8) (b) (6, 4) (c) (8, 10) (d) (20, 16)
  3. 3.What is the midpoint of the line joining (6, 10) and (16, 0)? (a) (5, 5) (b) (22, 10) (c) (5, 11) (d) (11, 5)
  4. 4.In which quadrant does the point (−6, 8) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  5. 5.What is the distance between the points (0, 2) and (9, 14)? (a) 16 (b) 225 (c) 21 (d) 15
  6. 6.What is the midpoint of the line joining (10, 7) and (18, 3)? (a) (28, 10) (b) (4, 2) (c) (14, 5) (d) (5, 14)
  7. 7.In which quadrant does the point (−3, 6) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  8. 8.What is the midpoint of the line joining (0, 8) and (8, 6)? (a) (4, 7) (b) (7, 4) (c) (8, 14) (d) (4, 1)
  9. 9.What is the distance between the points (5, 17) and (11, 9)? (a) 10 (b) 100 (c) 14 (d) 11
  10. 10.How far is the point (24, 7) from the origin (0, 0)? (a) 26 (b) 625 (c) 31 (d) 25
  11. 11.What is the midpoint of the line joining (4, 6) and (6, 16)? (a) (10, 22) (b) (5, 11) (c) (1, 5) (d) (11, 5)
  12. 12.In which quadrant does the point (−2, 3) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  13. 13.What is the distance between the points (7, 7) and (23, 19)? (a) 400 (b) 21 (c) 28 (d) 20
  14. 14.In which quadrant does the point (−4, −6) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  15. 15.What is the distance between the points (0, 2) and (16, 14)? (a) 20 (b) 28 (c) 400 (d) 21
  16. 16.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 21 (c) 20 (d) 28
  17. 17.In which quadrant does the point (−2, −6) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  18. 18.In which quadrant does the point (−6, 2) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  19. 19.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 5 (c) 25 (d) 7
  20. 20.What is the midpoint of the line joining (4, 2) and (8, 10)? (a) (12, 12) (b) (6, 6) (c) (2, 4) (d) (7, 6)
  21. 21.What is the distance between the points (5, 4) and (12, 28)? (a) 26 (b) 25 (c) 31 (d) 625
  22. 22.What is the distance between the points (0, 4) and (12, 20)? (a) 21 (b) 28 (c) 400 (d) 20
  23. 23.In which quadrant does the point (−9, 2) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  24. 24.What is the midpoint of the line joining (9, 7) and (19, 1)? (a) (28, 8) (b) (14, 4) (c) (5, 3) (d) (4, 14)
  25. 25.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 10 (c) 11 (d) 100
  26. 26.What is the distance between the points (7, 10) and (22, 2)? (a) 23 (b) 289 (c) 18 (d) 17
  27. 27.What is the midpoint of the line joining (7, 5) and (19, 17)? (a) (6, 6) (b) (11, 13) (c) (26, 22) (d) (13, 11)
  28. 28.What is the distance between the points (9, 24) and (16, 0)? (a) 625 (b) 25 (c) 31 (d) 26
  29. 29.What is the distance between the points (4, 4) and (8, 1)? (a) 6 (b) 25 (c) 7 (d) 5
  30. 30.What is the midpoint of the line joining (4, 4) and (12, 6)? (a) (5, 8) (b) (4, 1) (c) (16, 10) (d) (8, 5)
  31. 31.What is the midpoint of the line joining (9, 12) and (19, 0)? (a) (28, 12) (b) (14, 6) (c) (5, 6) (d) (6, 14)
  32. 32.What is the distance between the points (3, 3) and (7, 6)? (a) 5 (b) 6 (c) 7 (d) 25
  33. 33.What is the distance between the points (3, 15) and (9, 7)? (a) 11 (b) 100 (c) 10 (d) 14
  34. 34.What is the distance between the points (4, 5) and (13, 17)? (a) 16 (b) 15 (c) 225 (d) 21
  35. 35.What is the distance between the points (1, 9) and (9, 24)? (a) 289 (b) 23 (c) 18 (d) 17
  36. 36.What is the midpoint of the line joining (6, 9) and (16, 19)? (a) (5, 5) (b) (11, 14) (c) (14, 11) (d) (22, 28)
  37. 37.What is the distance between the points (7, 14) and (23, 2)? (a) 20 (b) 400 (c) 21 (d) 28
  38. 38.In which quadrant does the point (1, −2) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  39. 39.What is the midpoint of the line joining (6, 11) and (8, 9)? (a) (14, 20) (b) (10, 7) (c) (1, 1) (d) (7, 10)
  40. 40.In which quadrant does the point (−7, 2) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant

Answer key

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

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