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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 758 · 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 (5, −5) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  2. 2.What is the distance between the points (5, 2) and (13, 17)? (a) 23 (b) 18 (c) 17 (d) 289
  3. 3.In which quadrant does the point (7, 4) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  4. 4.What is the distance between the points (0, 0) and (3, 4)? (a) 25 (b) 5 (c) 6 (d) 7
  5. 5.In which quadrant does the point (−5, −9) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  6. 6.How far is the point (24, 7) from the origin (0, 0)? (a) 25 (b) 31 (c) 26 (d) 625
  7. 7.What is the midpoint of the line joining (6, 2) and (8, 4)? (a) (1, 1) (b) (14, 6) (c) (7, 3) (d) (3, 7)
  8. 8.What is the midpoint of the line joining (2, 9) and (6, 1)? (a) (8, 10) (b) (4, 5) (c) (5, 4) (d) (2, 4)
  9. 9.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 21 (c) 15 (d) 16
  10. 10.In which quadrant does the point (2, −7) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  11. 11.What is the distance between the points (4, 1) and (19, 9)? (a) 17 (b) 289 (c) 23 (d) 18
  12. 12.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 5 (c) 25 (d) 6
  13. 13.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 6 (c) 7 (d) 5
  14. 14.What is the distance between the points (8, 21) and (24, 9)? (a) 28 (b) 21 (c) 20 (d) 400
  15. 15.In which quadrant does the point (6, 9) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  16. 16.What is the distance between the points (8, 0) and (13, 12)? (a) 14 (b) 169 (c) 17 (d) 13
  17. 17.What is the distance between the points (8, 5) and (20, 21)? (a) 400 (b) 21 (c) 28 (d) 20
  18. 18.What is the midpoint of the line joining (4, 14) and (8, 4)? (a) (2, 5) (b) (9, 6) (c) (12, 18) (d) (6, 9)
  19. 19.In which quadrant does the point (−3, −4) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  20. 20.What is the distance between the points (0, 7) and (12, 2)? (a) 17 (b) 169 (c) 14 (d) 13
  21. 21.What is the distance between the points (6, 9) and (10, 12)? (a) 7 (b) 25 (c) 6 (d) 5
  22. 22.How far is the point (5, 12) from the origin (0, 0)? (a) 13 (b) 169 (c) 17 (d) 14
  23. 23.What is the distance between the points (9, 4) and (12, 0)? (a) 7 (b) 6 (c) 25 (d) 5
  24. 24.What is the midpoint of the line joining (5, 10) and (7, 0)? (a) (6, 5) (b) (12, 10) (c) (5, 6) (d) (1, 5)
  25. 25.What is the midpoint of the line joining (5, 6) and (13, 4)? (a) (4, 1) (b) (9, 5) (c) (5, 9) (d) (18, 10)
  26. 26.What is the midpoint of the line joining (5, 9) and (13, 3)? (a) (6, 9) (b) (18, 12) (c) (9, 6) (d) (4, 3)
  27. 27.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 11 (c) 14 (d) 10
  28. 28.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 10 (c) 11 (d) 14
  29. 29.In which quadrant does the point (5, −2) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  30. 30.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 17 (c) 18 (d) 23
  31. 31.What is the midpoint of the line joining (0, 21) and (8, 9)? (a) (8, 30) (b) (15, 4) (c) (4, 15) (d) (4, 6)
  32. 32.What is the distance between the points (1, 3) and (9, 18)? (a) 289 (b) 17 (c) 23 (d) 18
  33. 33.In which quadrant does the point (−7, 8) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  34. 34.What is the midpoint of the line joining (4, 8) and (10, 16)? (a) (3, 4) (b) (12, 7) (c) (14, 24) (d) (7, 12)
  35. 35.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 14 (c) 169 (d) 13
  36. 36.What is the midpoint of the line joining (2, 1) and (10, 9)? (a) (4, 4) (b) (5, 6) (c) (6, 5) (d) (12, 10)
  37. 37.In which quadrant does the point (−8, −1) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  38. 38.What is the distance between the points (2, 2) and (11, 14)? (a) 21 (b) 225 (c) 16 (d) 15
  39. 39.What is the midpoint of the line joining (6, 20) and (12, 8)? (a) (3, 6) (b) (9, 14) (c) (14, 9) (d) (18, 28)
  40. 40.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 21 (c) 400 (d) 28

Answer key

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

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