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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 859 · 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) 20 (b) 28 (c) 21 (d) 400
  2. 2.What is the distance between the points (2, 0) and (10, 6)? (a) 11 (b) 14 (c) 10 (d) 100
  3. 3.What is the midpoint of the line joining (0, 15) and (4, 5)? (a) (10, 2) (b) (4, 20) (c) (2, 5) (d) (2, 10)
  4. 4.What is the distance between the points (6, 21) and (18, 5)? (a) 21 (b) 28 (c) 20 (d) 400
  5. 5.In which quadrant does the point (−2, 4) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  6. 6.What is the midpoint of the line joining (9, 7) and (13, 13)? (a) (2, 3) (b) (10, 11) (c) (22, 20) (d) (11, 10)
  7. 7.In which quadrant does the point (4, 1) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  8. 8.What is the distance between the points (4, 8) and (12, 2)? (a) 11 (b) 14 (c) 10 (d) 100
  9. 9.What is the distance between the points (9, 8) and (21, 13)? (a) 17 (b) 169 (c) 14 (d) 13
  10. 10.What is the midpoint of the line joining (9, 15) and (17, 7)? (a) (26, 22) (b) (4, 4) (c) (13, 11) (d) (11, 13)
  11. 11.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 15 (c) 225 (d) 16
  12. 12.What is the distance between the points (4, 17) and (10, 9)? (a) 100 (b) 10 (c) 14 (d) 11
  13. 13.In which quadrant does the point (−6, −2) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  14. 14.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 28 (c) 20 (d) 400
  15. 15.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 25 (c) 5 (d) 7
  16. 16.What is the midpoint of the line joining (1, 8) and (7, 4)? (a) (8, 12) (b) (4, 6) (c) (3, 2) (d) (6, 4)
  17. 17.In which quadrant does the point (−8, −9) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  18. 18.In which quadrant does the point (−3, −7) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  19. 19.What is the distance between the points (5, 15) and (11, 7)? (a) 10 (b) 100 (c) 14 (d) 11
  20. 20.In which quadrant does the point (−6, 9) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  21. 21.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 289 (c) 23 (d) 18
  22. 22.What is the midpoint of the line joining (0, 6) and (2, 14)? (a) (10, 1) (b) (2, 20) (c) (1, 4) (d) (1, 10)
  23. 23.What is the distance between the points (5, 5) and (17, 0)? (a) 17 (b) 169 (c) 13 (d) 14
  24. 24.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 5 (c) 25 (d) 7
  25. 25.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 23 (c) 18 (d) 17
  26. 26.What is the midpoint of the line joining (5, 2) and (7, 8)? (a) (6, 5) (b) (12, 10) (c) (1, 3) (d) (5, 6)
  27. 27.In which quadrant does the point (−9, 6) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  28. 28.In which quadrant does the point (−6, 7) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  29. 29.What is the midpoint of the line joining (6, 7) and (18, 9)? (a) (6, 1) (b) (24, 16) (c) (12, 8) (d) (8, 12)
  30. 30.In which quadrant does the point (2, −9) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  31. 31.What is the midpoint of the line joining (2, 17) and (14, 5)? (a) (16, 22) (b) (6, 6) (c) (11, 8) (d) (8, 11)
  32. 32.What is the distance between the points (6, 8) and (12, 0)? (a) 100 (b) 11 (c) 14 (d) 10
  33. 33.What is the midpoint of the line joining (1, 11) and (5, 3)? (a) (7, 3) (b) (6, 14) (c) (3, 7) (d) (2, 4)
  34. 34.What is the distance between the points (1, 9) and (13, 0)? (a) 225 (b) 21 (c) 15 (d) 16
  35. 35.What is the distance between the points (0, 0) and (3, 4)? (a) 25 (b) 6 (c) 5 (d) 7
  36. 36.In which quadrant does the point (7, −9) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  37. 37.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 31 (c) 26 (d) 25
  38. 38.What is the distance between the points (6, 29) and (13, 5)? (a) 26 (b) 31 (c) 25 (d) 625
  39. 39.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 14 (c) 11 (d) 10
  40. 40.What is the midpoint of the line joining (2, 20) and (12, 10)? (a) (15, 7) (b) (5, 5) (c) (7, 15) (d) (14, 30)

Answer key

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

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