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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 999 · 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 (8, 12) and (16, 6)? (a) 10 (b) 100 (c) 14 (d) 11
  2. 2.What is the distance between the points (4, 7) and (28, 14)? (a) 26 (b) 25 (c) 625 (d) 31
  3. 3.What is the distance between the points (8, 9) and (23, 1)? (a) 289 (b) 18 (c) 17 (d) 23
  4. 4.What is the distance between the points (3, 7) and (15, 16)? (a) 225 (b) 21 (c) 16 (d) 15
  5. 5.What is the distance between the points (6, 0) and (14, 6)? (a) 100 (b) 14 (c) 11 (d) 10
  6. 6.What is the distance between the points (2, 17) and (7, 5)? (a) 17 (b) 13 (c) 14 (d) 169
  7. 7.In which quadrant does the point (8, 1) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  8. 8.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 25 (c) 625 (d) 26
  9. 9.In which quadrant does the point (−2, 4) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  10. 10.What is the distance between the points (8, 17) and (20, 1)? (a) 400 (b) 28 (c) 20 (d) 21
  11. 11.What is the distance between the points (4, 9) and (7, 13)? (a) 5 (b) 6 (c) 25 (d) 7
  12. 12.What is the distance between the points (2, 5) and (7, 17)? (a) 14 (b) 13 (c) 169 (d) 17
  13. 13.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 100 (c) 11 (d) 10
  14. 14.In which quadrant does the point (5, −5) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  15. 15.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 169 (c) 14 (d) 13
  16. 16.What is the midpoint of the line joining (6, 2) and (10, 10)? (a) (8, 6) (b) (16, 12) (c) (2, 4) (d) (6, 8)
  17. 17.In which quadrant does the point (−3, −6) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  18. 18.What is the distance between the points (2, 9) and (18, 21)? (a) 21 (b) 28 (c) 20 (d) 400
  19. 19.What is the distance between the points (0, 2) and (12, 7)? (a) 169 (b) 17 (c) 13 (d) 14
  20. 20.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 5 (c) 7 (d) 25
  21. 21.What is the midpoint of the line joining (2, 4) and (12, 2)? (a) (5, 1) (b) (14, 6) (c) (7, 3) (d) (3, 7)
  22. 22.What is the distance between the points (8, 5) and (16, 20)? (a) 289 (b) 17 (c) 23 (d) 18
  23. 23.What is the midpoint of the line joining (8, 1) and (14, 13)? (a) (3, 6) (b) (11, 7) (c) (22, 14) (d) (7, 11)
  24. 24.How far is the point (12, 16) from the origin (0, 0)? (a) 20 (b) 21 (c) 28 (d) 400
  25. 25.What is the midpoint of the line joining (0, 9) and (8, 19)? (a) (8, 28) (b) (4, 5) (c) (4, 14) (d) (14, 4)
  26. 26.What is the distance between the points (5, 7) and (11, 15)? (a) 100 (b) 10 (c) 11 (d) 14
  27. 27.In which quadrant does the point (3, −1) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  28. 28.What is the midpoint of the line joining (3, 12) and (9, 0)? (a) (12, 12) (b) (6, 6) (c) (3, 6) (d) (7, 6)
  29. 29.In which quadrant does the point (−4, 8) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  30. 30.What is the distance between the points (8, 1) and (12, 4)? (a) 7 (b) 5 (c) 6 (d) 25
  31. 31.What is the distance between the points (6, 12) and (9, 8)? (a) 25 (b) 5 (c) 6 (d) 7
  32. 32.What is the midpoint of the line joining (0, 0) and (6, 10)? (a) (3, 5) (b) (6, 10) (c) (4, 5) (d) (5, 3)
  33. 33.In which quadrant does the point (−5, −4) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  34. 34.What is the distance between the points (2, 1) and (9, 25)? (a) 625 (b) 25 (c) 31 (d) 26
  35. 35.What is the distance between the points (2, 16) and (18, 4)? (a) 400 (b) 20 (c) 21 (d) 28
  36. 36.In which quadrant does the point (1, 1) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  37. 37.In which quadrant does the point (−3, −3) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  38. 38.What is the distance between the points (7, 1) and (19, 6)? (a) 14 (b) 17 (c) 13 (d) 169
  39. 39.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 13 (c) 169 (d) 17
  40. 40.What is the distance between the points (2, 7) and (10, 22)? (a) 289 (b) 23 (c) 18 (d) 17

Answer key

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

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