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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 760 · 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 (2, 17) and (4, 7)? (a) (3, 12) (b) (1, 5) (c) (6, 24) (d) (12, 3)
  2. 2.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 100 (c) 10 (d) 14
  3. 3.In which quadrant does the point (1, 7) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  4. 4.What is the midpoint of the line joining (1, 7) and (5, 15)? (a) (3, 11) (b) (11, 3) (c) (6, 22) (d) (2, 4)
  5. 5.What is the midpoint of the line joining (0, 3) and (6, 1)? (a) (6, 4) (b) (3, 1) (c) (3, 2) (d) (2, 3)
  6. 6.What is the distance between the points (7, 5) and (16, 17)? (a) 21 (b) 16 (c) 225 (d) 15
  7. 7.What is the midpoint of the line joining (0, 6) and (6, 2)? (a) (6, 8) (b) (4, 3) (c) (3, 4) (d) (3, 2)
  8. 8.In which quadrant does the point (1, 3) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  9. 9.What is the distance between the points (0, 25) and (12, 9)? (a) 28 (b) 400 (c) 20 (d) 21
  10. 10.What is the distance between the points (4, 12) and (12, 6)? (a) 100 (b) 10 (c) 11 (d) 14
  11. 11.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 20 (c) 28 (d) 21
  12. 12.What is the midpoint of the line joining (9, 2) and (15, 4)? (a) (3, 1) (b) (12, 3) (c) (3, 12) (d) (24, 6)
  13. 13.What is the distance between the points (0, 11) and (6, 3)? (a) 14 (b) 100 (c) 11 (d) 10
  14. 14.What is the midpoint of the line joining (0, 13) and (6, 9)? (a) (3, 2) (b) (11, 3) (c) (3, 11) (d) (6, 22)
  15. 15.What is the distance between the points (9, 10) and (21, 5)? (a) 13 (b) 14 (c) 169 (d) 17
  16. 16.What is the distance between the points (9, 31) and (16, 7)? (a) 31 (b) 25 (c) 26 (d) 625
  17. 17.What is the distance between the points (6, 8) and (14, 23)? (a) 18 (b) 23 (c) 289 (d) 17
  18. 18.How far is the point (12, 5) from the origin (0, 0)? (a) 13 (b) 169 (c) 14 (d) 17
  19. 19.In which quadrant does the point (−7, −1) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  20. 20.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 23 (c) 17 (d) 18
  21. 21.What is the distance between the points (1, 22) and (13, 6)? (a) 20 (b) 400 (c) 28 (d) 21
  22. 22.What is the distance between the points (6, 7) and (10, 10)? (a) 6 (b) 25 (c) 5 (d) 7
  23. 23.What is the distance between the points (4, 25) and (11, 1)? (a) 25 (b) 625 (c) 26 (d) 31
  24. 24.In which quadrant does the point (7, −9) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  25. 25.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 14 (c) 10 (d) 11
  26. 26.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 289 (c) 17 (d) 23
  27. 27.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 15 (c) 16 (d) 225
  28. 28.What is the midpoint of the line joining (10, 5) and (16, 9)? (a) (3, 2) (b) (7, 13) (c) (13, 7) (d) (26, 14)
  29. 29.What is the midpoint of the line joining (9, 2) and (11, 6)? (a) (10, 4) (b) (4, 10) (c) (1, 2) (d) (20, 8)
  30. 30.In which quadrant does the point (−1, −6) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  31. 31.What is the distance between the points (4, 22) and (12, 7)? (a) 23 (b) 18 (c) 289 (d) 17
  32. 32.What is the midpoint of the line joining (5, 11) and (13, 3)? (a) (18, 14) (b) (4, 4) (c) (9, 7) (d) (7, 9)
  33. 33.How far is the point (5, 12) from the origin (0, 0)? (a) 13 (b) 14 (c) 169 (d) 17
  34. 34.What is the distance between the points (4, 1) and (12, 16)? (a) 23 (b) 17 (c) 18 (d) 289
  35. 35.What is the distance between the points (0, 4) and (3, 8)? (a) 7 (b) 5 (c) 6 (d) 25
  36. 36.In which quadrant does the point (−9, −3) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  37. 37.What is the midpoint of the line joining (6, 10) and (8, 22)? (a) (1, 6) (b) (16, 7) (c) (7, 16) (d) (14, 32)
  38. 38.What is the midpoint of the line joining (9, 12) and (17, 0)? (a) (6, 13) (b) (4, 6) (c) (26, 12) (d) (13, 6)
  39. 39.In which quadrant does the point (−7, 4) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  40. 40.What is the midpoint of the line joining (8, 3) and (20, 15)? (a) (6, 6) (b) (9, 14) (c) (14, 9) (d) (28, 18)

Answer key

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

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