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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 699 · 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 (15, 8) from the origin (0, 0)? (a) 23 (b) 18 (c) 289 (d) 17
  2. 2.In which quadrant does the point (−1, −4) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  3. 3.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 10 (c) 11 (d) 14
  4. 4.What is the midpoint of the line joining (7, 6) and (13, 12)? (a) (9, 10) (b) (10, 9) (c) (20, 18) (d) (3, 3)
  5. 5.What is the distance between the points (5, 9) and (29, 16)? (a) 25 (b) 625 (c) 26 (d) 31
  6. 6.In which quadrant does the point (6, 6) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  7. 7.In which quadrant does the point (9, 9) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  8. 8.In which quadrant does the point (5, 3) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  9. 9.In which quadrant does the point (−2, −1) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  10. 10.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 25 (c) 6 (d) 5
  11. 11.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 400 (c) 20 (d) 28
  12. 12.In which quadrant does the point (3, −3) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  13. 13.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 13 (c) 17 (d) 169
  14. 14.What is the distance between the points (2, 0) and (17, 8)? (a) 23 (b) 289 (c) 17 (d) 18
  15. 15.What is the distance between the points (7, 6) and (16, 18)? (a) 15 (b) 225 (c) 16 (d) 21
  16. 16.What is the midpoint of the line joining (2, 5) and (12, 13)? (a) (9, 7) (b) (7, 9) (c) (14, 18) (d) (5, 4)
  17. 17.What is the distance between the points (6, 6) and (14, 0)? (a) 100 (b) 11 (c) 14 (d) 10
  18. 18.In which quadrant does the point (−5, −7) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  19. 19.What is the distance between the points (4, 11) and (19, 3)? (a) 18 (b) 23 (c) 17 (d) 289
  20. 20.How far is the point (24, 7) from the origin (0, 0)? (a) 26 (b) 31 (c) 625 (d) 25
  21. 21.What is the midpoint of the line joining (3, 6) and (7, 10)? (a) (5, 8) (b) (10, 16) (c) (8, 5) (d) (2, 2)
  22. 22.What is the midpoint of the line joining (6, 6) and (18, 12)? (a) (24, 18) (b) (6, 3) (c) (9, 12) (d) (12, 9)
  23. 23.What is the midpoint of the line joining (8, 0) and (20, 4)? (a) (14, 2) (b) (6, 2) (c) (28, 4) (d) (2, 14)
  24. 24.What is the distance between the points (5, 1) and (17, 10)? (a) 225 (b) 15 (c) 16 (d) 21
  25. 25.What is the distance between the points (9, 2) and (25, 14)? (a) 28 (b) 400 (c) 21 (d) 20
  26. 26.What is the distance between the points (5, 11) and (11, 3)? (a) 14 (b) 100 (c) 10 (d) 11
  27. 27.What is the midpoint of the line joining (1, 4) and (7, 6)? (a) (4, 5) (b) (5, 4) (c) (8, 10) (d) (3, 1)
  28. 28.What is the midpoint of the line joining (2, 20) and (14, 8)? (a) (16, 28) (b) (14, 8) (c) (6, 6) (d) (8, 14)
  29. 29.What is the distance between the points (0, 24) and (8, 9)? (a) 17 (b) 23 (c) 18 (d) 289
  30. 30.In which quadrant does the point (−7, −5) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  31. 31.What is the distance between the points (0, 7) and (6, 15)? (a) 11 (b) 14 (c) 100 (d) 10
  32. 32.In which quadrant does the point (−6, 3) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  33. 33.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 100 (c) 10 (d) 11
  34. 34.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 31 (c) 25 (d) 625
  35. 35.In which quadrant does the point (1, −1) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  36. 36.In which quadrant does the point (−8, −7) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  37. 37.What is the distance between the points (6, 27) and (13, 3)? (a) 26 (b) 25 (c) 625 (d) 31
  38. 38.What is the distance between the points (3, 16) and (12, 4)? (a) 21 (b) 15 (c) 225 (d) 16
  39. 39.What is the distance between the points (2, 0) and (7, 12)? (a) 17 (b) 14 (c) 169 (d) 13
  40. 40.In which quadrant does the point (3, 3) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant

Answer key

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

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