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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 138 · 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 (4, −6) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  2. 2.What is the distance between the points (9, 12) and (14, 0)? (a) 14 (b) 169 (c) 17 (d) 13
  3. 3.What is the distance between the points (0, 7) and (3, 11)? (a) 6 (b) 5 (c) 7 (d) 25
  4. 4.What is the distance between the points (3, 6) and (9, 14)? (a) 100 (b) 10 (c) 11 (d) 14
  5. 5.What is the midpoint of the line joining (2, 18) and (10, 6)? (a) (12, 24) (b) (12, 6) (c) (6, 12) (d) (4, 6)
  6. 6.What is the distance between the points (2, 18) and (18, 6)? (a) 28 (b) 21 (c) 20 (d) 400
  7. 7.What is the midpoint of the line joining (4, 12) and (16, 10)? (a) (20, 22) (b) (11, 10) (c) (10, 11) (d) (6, 1)
  8. 8.What is the distance between the points (8, 3) and (23, 11)? (a) 18 (b) 289 (c) 17 (d) 23
  9. 9.What is the distance between the points (0, 9) and (6, 17)? (a) 14 (b) 11 (c) 100 (d) 10
  10. 10.In which quadrant does the point (−2, 5) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  11. 11.What is the distance between the points (7, 7) and (31, 14)? (a) 31 (b) 625 (c) 26 (d) 25
  12. 12.What is the midpoint of the line joining (7, 3) and (13, 13)? (a) (8, 10) (b) (20, 16) (c) (10, 8) (d) (3, 5)
  13. 13.In which quadrant does the point (−1, 1) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  14. 14.What is the distance between the points (5, 8) and (13, 14)? (a) 14 (b) 100 (c) 10 (d) 11
  15. 15.What is the distance between the points (3, 7) and (11, 22)? (a) 23 (b) 17 (c) 18 (d) 289
  16. 16.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 31 (c) 25 (d) 26
  17. 17.What is the distance between the points (3, 7) and (11, 1)? (a) 14 (b) 100 (c) 10 (d) 11
  18. 18.What is the distance between the points (0, 11) and (12, 2)? (a) 16 (b) 15 (c) 225 (d) 21
  19. 19.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 5 (c) 6 (d) 7
  20. 20.What is the distance between the points (7, 14) and (19, 9)? (a) 17 (b) 14 (c) 169 (d) 13
  21. 21.What is the distance between the points (3, 24) and (11, 9)? (a) 17 (b) 23 (c) 289 (d) 18
  22. 22.What is the midpoint of the line joining (8, 13) and (14, 1)? (a) (11, 7) (b) (7, 11) (c) (3, 6) (d) (22, 14)
  23. 23.What is the midpoint of the line joining (4, 6) and (10, 12)? (a) (9, 7) (b) (3, 3) (c) (14, 18) (d) (7, 9)
  24. 24.What is the midpoint of the line joining (1, 4) and (7, 8)? (a) (8, 12) (b) (4, 6) (c) (3, 2) (d) (6, 4)
  25. 25.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 7 (c) 5 (d) 25
  26. 26.What is the distance between the points (3, 15) and (8, 3)? (a) 14 (b) 13 (c) 169 (d) 17
  27. 27.What is the distance between the points (0, 8) and (24, 15)? (a) 31 (b) 26 (c) 25 (d) 625
  28. 28.What is the distance between the points (9, 8) and (16, 32)? (a) 26 (b) 31 (c) 25 (d) 625
  29. 29.In which quadrant does the point (−6, −5) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  30. 30.What is the midpoint of the line joining (0, 7) and (4, 17)? (a) (12, 2) (b) (4, 24) (c) (2, 5) (d) (2, 12)
  31. 31.What is the distance between the points (0, 17) and (12, 1)? (a) 28 (b) 21 (c) 400 (d) 20
  32. 32.In which quadrant does the point (−1, −6) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  33. 33.What is the midpoint of the line joining (10, 10) and (12, 8)? (a) (9, 11) (b) (11, 9) (c) (22, 18) (d) (1, 1)
  34. 34.What is the midpoint of the line joining (10, 12) and (20, 0)? (a) (6, 15) (b) (5, 6) (c) (15, 6) (d) (30, 12)
  35. 35.What is the distance between the points (0, 10) and (4, 7)? (a) 7 (b) 25 (c) 6 (d) 5
  36. 36.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 28 (c) 400 (d) 20
  37. 37.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 10 (c) 14 (d) 11
  38. 38.What is the midpoint of the line joining (5, 14) and (9, 4)? (a) (7, 9) (b) (14, 18) (c) (2, 5) (d) (9, 7)
  39. 39.In which quadrant does the point (−6, −8) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  40. 40.What is the distance between the points (5, 16) and (13, 1)? (a) 289 (b) 23 (c) 18 (d) 17

Answer key

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

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