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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 887 · 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 (2, 11) and (26, 4)? (a) 31 (b) 625 (c) 26 (d) 25
  2. 2.In which quadrant does the point (−6, −7) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  3. 3.What is the midpoint of the line joining (0, 8) and (4, 12)? (a) (2, 10) (b) (2, 2) (c) (10, 2) (d) (4, 20)
  4. 4.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 625 (c) 25 (d) 26
  5. 5.In which quadrant does the point (−5, 3) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  6. 6.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 5 (c) 7 (d) 6
  7. 7.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 169 (c) 13 (d) 14
  8. 8.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 100 (c) 14 (d) 11
  9. 9.In which quadrant does the point (−7, −3) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  10. 10.In which quadrant does the point (−5, 8) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  11. 11.What is the distance between the points (8, 1) and (13, 13)? (a) 17 (b) 13 (c) 169 (d) 14
  12. 12.In which quadrant does the point (−9, 7) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  13. 13.In which quadrant does the point (−3, −2) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  14. 14.What is the midpoint of the line joining (7, 2) and (19, 0)? (a) (13, 1) (b) (1, 13) (c) (6, 1) (d) (26, 2)
  15. 15.What is the distance between the points (3, 3) and (15, 12)? (a) 16 (b) 21 (c) 225 (d) 15
  16. 16.What is the midpoint of the line joining (3, 9) and (11, 17)? (a) (7, 13) (b) (4, 4) (c) (13, 7) (d) (14, 26)
  17. 17.What is the distance between the points (5, 0) and (13, 15)? (a) 17 (b) 23 (c) 289 (d) 18
  18. 18.In which quadrant does the point (5, −4) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  19. 19.What is the midpoint of the line joining (8, 10) and (10, 16)? (a) (1, 3) (b) (13, 9) (c) (9, 13) (d) (18, 26)
  20. 20.What is the midpoint of the line joining (9, 6) and (19, 10)? (a) (8, 14) (b) (5, 2) (c) (28, 16) (d) (14, 8)
  21. 21.What is the distance between the points (1, 8) and (5, 11)? (a) 5 (b) 7 (c) 6 (d) 25
  22. 22.In which quadrant does the point (7, 4) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  23. 23.What is the midpoint of the line joining (3, 3) and (5, 5)? (a) (8, 8) (b) (1, 1) (c) (5, 4) (d) (4, 4)
  24. 24.What is the midpoint of the line joining (0, 9) and (2, 11)? (a) (1, 10) (b) (2, 20) (c) (1, 1) (d) (10, 1)
  25. 25.What is the midpoint of the line joining (2, 7) and (14, 3)? (a) (8, 5) (b) (6, 2) (c) (16, 10) (d) (5, 8)
  26. 26.What is the midpoint of the line joining (1, 17) and (13, 9)? (a) (14, 26) (b) (7, 13) (c) (13, 7) (d) (6, 4)
  27. 27.What is the distance between the points (4, 9) and (28, 16)? (a) 31 (b) 625 (c) 26 (d) 25
  28. 28.What is the midpoint of the line joining (9, 16) and (15, 8)? (a) (3, 4) (b) (12, 12) (c) (13, 12) (d) (24, 24)
  29. 29.What is the midpoint of the line joining (5, 2) and (9, 12)? (a) (7, 7) (b) (8, 7) (c) (2, 5) (d) (14, 14)
  30. 30.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 225 (c) 16 (d) 15
  31. 31.What is the midpoint of the line joining (9, 5) and (11, 13)? (a) (1, 4) (b) (10, 9) (c) (20, 18) (d) (9, 10)
  32. 32.What is the distance between the points (5, 8) and (29, 1)? (a) 31 (b) 26 (c) 625 (d) 25
  33. 33.What is the midpoint of the line joining (3, 3) and (5, 13)? (a) (8, 16) (b) (1, 5) (c) (8, 4) (d) (4, 8)
  34. 34.What is the midpoint of the line joining (7, 19) and (19, 9)? (a) (26, 28) (b) (6, 5) (c) (13, 14) (d) (14, 13)
  35. 35.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 14 (c) 17 (d) 13
  36. 36.What is the distance between the points (4, 12) and (12, 6)? (a) 11 (b) 14 (c) 100 (d) 10
  37. 37.In which quadrant does the point (−3, 7) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  38. 38.What is the distance between the points (3, 7) and (9, 15)? (a) 14 (b) 100 (c) 10 (d) 11
  39. 39.In which quadrant does the point (6, 9) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  40. 40.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 100 (c) 11 (d) 14

Answer key

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

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