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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 486 · 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 (1, 15) and (5, 9)? (a) (2, 3) (b) (12, 3) (c) (3, 12) (d) (6, 24)
  2. 2.What is the distance between the points (3, 14) and (27, 7)? (a) 26 (b) 31 (c) 25 (d) 625
  3. 3.In which quadrant does the point (−3, −9) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  4. 4.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 18 (c) 17 (d) 289
  5. 5.What is the midpoint of the line joining (2, 4) and (8, 0)? (a) (2, 5) (b) (3, 2) (c) (10, 4) (d) (5, 2)
  6. 6.What is the distance between the points (4, 4) and (16, 20)? (a) 400 (b) 28 (c) 20 (d) 21
  7. 7.What is the distance between the points (2, 0) and (7, 12)? (a) 169 (b) 13 (c) 14 (d) 17
  8. 8.In which quadrant does the point (1, −8) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  9. 9.What is the midpoint of the line joining (4, 10) and (6, 12)? (a) (1, 1) (b) (5, 11) (c) (11, 5) (d) (10, 22)
  10. 10.What is the distance between the points (8, 12) and (12, 9)? (a) 5 (b) 25 (c) 7 (d) 6
  11. 11.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 400 (c) 21 (d) 28
  12. 12.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 17 (c) 289 (d) 18
  13. 13.In which quadrant does the point (−4, −3) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  14. 14.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 225 (c) 21 (d) 15
  15. 15.What is the distance between the points (9, 7) and (12, 11)? (a) 6 (b) 7 (c) 5 (d) 25
  16. 16.In which quadrant does the point (−2, −6) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  17. 17.What is the midpoint of the line joining (9, 21) and (15, 9)? (a) (12, 15) (b) (24, 30) (c) (15, 12) (d) (3, 6)
  18. 18.In which quadrant does the point (6, −6) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  19. 19.What is the midpoint of the line joining (8, 7) and (20, 13)? (a) (6, 3) (b) (28, 20) (c) (10, 14) (d) (14, 10)
  20. 20.How far is the point (5, 12) from the origin (0, 0)? (a) 13 (b) 14 (c) 169 (d) 17
  21. 21.In which quadrant does the point (−5, 5) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  22. 22.What is the distance between the points (4, 7) and (12, 22)? (a) 17 (b) 289 (c) 18 (d) 23
  23. 23.What is the midpoint of the line joining (4, 10) and (16, 2)? (a) (6, 10) (b) (20, 12) (c) (10, 6) (d) (6, 4)
  24. 24.What is the distance between the points (2, 0) and (18, 12)? (a) 28 (b) 20 (c) 21 (d) 400
  25. 25.What is the midpoint of the line joining (0, 3) and (12, 9)? (a) (6, 3) (b) (12, 12) (c) (6, 6) (d) (7, 6)
  26. 26.What is the distance between the points (5, 27) and (12, 3)? (a) 25 (b) 625 (c) 31 (d) 26
  27. 27.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 5 (c) 6 (d) 7
  28. 28.What is the distance between the points (0, 2) and (12, 11)? (a) 16 (b) 21 (c) 15 (d) 225
  29. 29.What is the midpoint of the line joining (2, 4) and (14, 10)? (a) (16, 14) (b) (8, 7) (c) (6, 3) (d) (7, 8)
  30. 30.In which quadrant does the point (−1, 2) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  31. 31.What is the midpoint of the line joining (1, 10) and (11, 2)? (a) (5, 4) (b) (7, 6) (c) (6, 6) (d) (12, 12)
  32. 32.What is the midpoint of the line joining (3, 22) and (7, 10)? (a) (2, 6) (b) (16, 5) (c) (10, 32) (d) (5, 16)
  33. 33.What is the midpoint of the line joining (9, 4) and (11, 10)? (a) (1, 3) (b) (20, 14) (c) (7, 10) (d) (10, 7)
  34. 34.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 10 (c) 100 (d) 11
  35. 35.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 11 (c) 10 (d) 14
  36. 36.What is the distance between the points (3, 13) and (12, 1)? (a) 21 (b) 16 (c) 225 (d) 15
  37. 37.What is the distance between the points (5, 6) and (21, 18)? (a) 400 (b) 28 (c) 20 (d) 21
  38. 38.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 225 (c) 16 (d) 15
  39. 39.In which quadrant does the point (5, 5) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  40. 40.What is the distance between the points (9, 2) and (17, 8)? (a) 100 (b) 11 (c) 10 (d) 14

Answer key

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

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