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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 310 · 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 midpoint of the line joining (0, 1) and (4, 11)? (a) (4, 12) (b) (2, 5) (c) (6, 2) (d) (2, 6)
  2. 2.In which quadrant does the point (−6, 6) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  3. 3.What is the distance between the points (5, 9) and (21, 21)? (a) 21 (b) 20 (c) 400 (d) 28
  4. 4.In which quadrant does the point (−4, 1) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  5. 5.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 25 (c) 7 (d) 5
  6. 6.What is the distance between the points (2, 13) and (26, 6)? (a) 31 (b) 26 (c) 25 (d) 625
  7. 7.In which quadrant does the point (−3, −6) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  8. 8.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 169 (c) 17 (d) 13
  9. 9.In which quadrant does the point (−5, −3) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  10. 10.In which quadrant does the point (−1, −7) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  11. 11.What is the midpoint of the line joining (2, 5) and (10, 7)? (a) (4, 1) (b) (7, 6) (c) (6, 6) (d) (12, 12)
  12. 12.How far is the point (15, 8) from the origin (0, 0)? (a) 17 (b) 289 (c) 23 (d) 18
  13. 13.What is the distance between the points (7, 14) and (19, 5)? (a) 21 (b) 16 (c) 225 (d) 15
  14. 14.What is the midpoint of the line joining (4, 8) and (12, 20)? (a) (4, 6) (b) (16, 28) (c) (14, 8) (d) (8, 14)
  15. 15.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 7 (c) 5 (d) 6
  16. 16.What is the midpoint of the line joining (7, 4) and (11, 2)? (a) (2, 1) (b) (18, 6) (c) (3, 9) (d) (9, 3)
  17. 17.What is the midpoint of the line joining (5, 2) and (17, 6)? (a) (22, 8) (b) (11, 4) (c) (4, 11) (d) (6, 2)
  18. 18.What is the midpoint of the line joining (1, 1) and (3, 7)? (a) (2, 4) (b) (4, 2) (c) (1, 3) (d) (4, 8)
  19. 19.What is the midpoint of the line joining (8, 0) and (20, 12)? (a) (14, 6) (b) (28, 12) (c) (6, 6) (d) (6, 14)
  20. 20.What is the distance between the points (8, 14) and (23, 6)? (a) 18 (b) 289 (c) 23 (d) 17
  21. 21.In which quadrant does the point (9, 3) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  22. 22.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 10 (c) 14 (d) 100
  23. 23.In which quadrant does the point (3, −5) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  24. 24.In which quadrant does the point (7, −6) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  25. 25.In which quadrant does the point (−4, −5) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  26. 26.What is the midpoint of the line joining (0, 14) and (12, 10)? (a) (12, 6) (b) (6, 2) (c) (12, 24) (d) (6, 12)
  27. 27.What is the distance between the points (0, 14) and (8, 8)? (a) 100 (b) 14 (c) 10 (d) 11
  28. 28.What is the distance between the points (5, 0) and (21, 12)? (a) 20 (b) 28 (c) 21 (d) 400
  29. 29.In which quadrant does the point (2, −3) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  30. 30.What is the midpoint of the line joining (4, 2) and (12, 8)? (a) (5, 8) (b) (4, 3) (c) (16, 10) (d) (8, 5)
  31. 31.What is the distance between the points (2, 0) and (6, 3)? (a) 6 (b) 25 (c) 7 (d) 5
  32. 32.In which quadrant does the point (−7, 7) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  33. 33.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 21 (c) 400 (d) 28
  34. 34.What is the distance between the points (5, 5) and (21, 17)? (a) 400 (b) 28 (c) 21 (d) 20
  35. 35.What is the distance between the points (1, 2) and (4, 6)? (a) 6 (b) 25 (c) 7 (d) 5
  36. 36.What is the midpoint of the line joining (6, 17) and (8, 9)? (a) (1, 4) (b) (14, 26) (c) (7, 13) (d) (13, 7)
  37. 37.What is the distance between the points (0, 4) and (9, 16)? (a) 21 (b) 225 (c) 16 (d) 15
  38. 38.In which quadrant does the point (−8, −5) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  39. 39.What is the distance between the points (7, 6) and (22, 14)? (a) 17 (b) 18 (c) 23 (d) 289
  40. 40.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 13 (c) 169 (d) 17

Answer key

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

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