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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 627 · 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, 8) and (16, 14)? (a) 11 (b) 14 (c) 10 (d) 100
  2. 2.In which quadrant does the point (1, −2) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  3. 3.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 225 (c) 16 (d) 15
  4. 4.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 5 (c) 6 (d) 25
  5. 5.What is the midpoint of the line joining (8, 7) and (10, 9)? (a) (8, 9) (b) (9, 8) (c) (1, 1) (d) (18, 16)
  6. 6.In which quadrant does the point (9, −2) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  7. 7.What is the midpoint of the line joining (8, 3) and (10, 7)? (a) (18, 10) (b) (9, 5) (c) (1, 2) (d) (5, 9)
  8. 8.What is the midpoint of the line joining (10, 10) and (14, 20)? (a) (24, 30) (b) (15, 12) (c) (12, 15) (d) (2, 5)
  9. 9.In which quadrant does the point (7, −6) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  10. 10.What is the distance between the points (0, 0) and (7, 24)? (a) 625 (b) 26 (c) 25 (d) 31
  11. 11.What is the midpoint of the line joining (8, 22) and (12, 10)? (a) (20, 32) (b) (16, 10) (c) (10, 16) (d) (2, 6)
  12. 12.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 13 (c) 169 (d) 17
  13. 13.What is the distance between the points (2, 15) and (17, 7)? (a) 23 (b) 17 (c) 289 (d) 18
  14. 14.What is the distance between the points (8, 9) and (32, 16)? (a) 625 (b) 25 (c) 26 (d) 31
  15. 15.What is the distance between the points (3, 10) and (11, 4)? (a) 14 (b) 10 (c) 11 (d) 100
  16. 16.What is the distance between the points (1, 24) and (9, 9)? (a) 289 (b) 17 (c) 23 (d) 18
  17. 17.What is the midpoint of the line joining (4, 4) and (8, 8)? (a) (7, 6) (b) (6, 6) (c) (2, 2) (d) (12, 12)
  18. 18.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 7 (c) 25 (d) 5
  19. 19.What is the distance between the points (2, 9) and (9, 33)? (a) 625 (b) 25 (c) 31 (d) 26
  20. 20.What is the midpoint of the line joining (8, 6) and (10, 8)? (a) (7, 9) (b) (9, 7) (c) (18, 14) (d) (1, 1)
  21. 21.What is the distance between the points (1, 3) and (8, 27)? (a) 625 (b) 31 (c) 26 (d) 25
  22. 22.What is the midpoint of the line joining (1, 4) and (7, 16)? (a) (8, 20) (b) (4, 10) (c) (3, 6) (d) (10, 4)
  23. 23.What is the midpoint of the line joining (2, 9) and (10, 3)? (a) (12, 12) (b) (6, 6) (c) (4, 3) (d) (7, 6)
  24. 24.What is the midpoint of the line joining (2, 4) and (4, 6)? (a) (1, 1) (b) (3, 5) (c) (5, 3) (d) (6, 10)
  25. 25.What is the midpoint of the line joining (2, 0) and (12, 12)? (a) (14, 12) (b) (7, 6) (c) (6, 7) (d) (5, 6)
  26. 26.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 25 (c) 26 (d) 625
  27. 27.In which quadrant does the point (1, −7) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  28. 28.What is the distance between the points (5, 4) and (9, 1)? (a) 25 (b) 6 (c) 5 (d) 7
  29. 29.What is the distance between the points (2, 2) and (17, 10)? (a) 17 (b) 289 (c) 18 (d) 23
  30. 30.What is the distance between the points (4, 8) and (12, 14)? (a) 100 (b) 10 (c) 11 (d) 14
  31. 31.What is the midpoint of the line joining (0, 10) and (10, 12)? (a) (11, 5) (b) (5, 11) (c) (10, 22) (d) (5, 1)
  32. 32.What is the distance between the points (9, 14) and (21, 5)? (a) 16 (b) 15 (c) 21 (d) 225
  33. 33.What is the distance between the points (9, 6) and (21, 22)? (a) 28 (b) 400 (c) 20 (d) 21
  34. 34.What is the midpoint of the line joining (8, 8) and (12, 14)? (a) (2, 3) (b) (10, 11) (c) (20, 22) (d) (11, 10)
  35. 35.In which quadrant does the point (−3, −5) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  36. 36.What is the midpoint of the line joining (10, 6) and (12, 2)? (a) (22, 8) (b) (11, 4) (c) (1, 2) (d) (4, 11)
  37. 37.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 13 (c) 169 (d) 17
  38. 38.What is the distance between the points (2, 3) and (8, 11)? (a) 10 (b) 11 (c) 14 (d) 100
  39. 39.What is the distance between the points (0, 6) and (15, 14)? (a) 23 (b) 18 (c) 17 (d) 289
  40. 40.What is the distance between the points (0, 12) and (8, 6)? (a) 100 (b) 11 (c) 14 (d) 10

Answer key

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

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