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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 281 · 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 (5, 4) and (13, 6)? (a) (18, 10) (b) (5, 9) (c) (9, 5) (d) (4, 1)
  2. 2.What is the distance between the points (4, 3) and (11, 27)? (a) 625 (b) 25 (c) 31 (d) 26
  3. 3.What is the midpoint of the line joining (0, 14) and (2, 2)? (a) (8, 1) (b) (1, 6) (c) (2, 16) (d) (1, 8)
  4. 4.How far is the point (12, 16) from the origin (0, 0)? (a) 20 (b) 21 (c) 28 (d) 400
  5. 5.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 400 (c) 20 (d) 21
  6. 6.How far is the point (15, 8) from the origin (0, 0)? (a) 17 (b) 289 (c) 23 (d) 18
  7. 7.What is the distance between the points (2, 12) and (14, 7)? (a) 169 (b) 14 (c) 13 (d) 17
  8. 8.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 7 (c) 6 (d) 5
  9. 9.What is the distance between the points (0, 8) and (12, 24)? (a) 28 (b) 400 (c) 21 (d) 20
  10. 10.What is the midpoint of the line joining (1, 7) and (11, 5)? (a) (5, 1) (b) (6, 6) (c) (7, 6) (d) (12, 12)
  11. 11.What is the midpoint of the line joining (10, 21) and (20, 9)? (a) (5, 6) (b) (16, 15) (c) (30, 30) (d) (15, 15)
  12. 12.What is the midpoint of the line joining (3, 13) and (7, 5)? (a) (2, 4) (b) (5, 9) (c) (9, 5) (d) (10, 18)
  13. 13.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 14 (c) 10 (d) 100
  14. 14.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 26 (c) 625 (d) 25
  15. 15.In which quadrant does the point (−8, −3) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  16. 16.What is the distance between the points (7, 4) and (23, 16)? (a) 20 (b) 21 (c) 400 (d) 28
  17. 17.What is the midpoint of the line joining (3, 4) and (9, 10)? (a) (12, 14) (b) (3, 3) (c) (6, 7) (d) (7, 6)
  18. 18.In which quadrant does the point (−9, 1) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  19. 19.What is the midpoint of the line joining (7, 13) and (11, 5)? (a) (10, 9) (b) (18, 18) (c) (2, 4) (d) (9, 9)
  20. 20.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 7 (c) 5 (d) 6
  21. 21.What is the midpoint of the line joining (7, 5) and (17, 7)? (a) (6, 12) (b) (24, 12) (c) (12, 6) (d) (5, 1)
  22. 22.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 17 (c) 289 (d) 23
  23. 23.What is the midpoint of the line joining (0, 8) and (2, 18)? (a) (1, 5) (b) (1, 13) (c) (2, 26) (d) (13, 1)
  24. 24.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 17 (c) 13 (d) 14
  25. 25.What is the midpoint of the line joining (9, 13) and (11, 5)? (a) (10, 9) (b) (1, 4) (c) (20, 18) (d) (9, 10)
  26. 26.What is the distance between the points (9, 8) and (16, 32)? (a) 625 (b) 26 (c) 31 (d) 25
  27. 27.How far is the point (12, 9) from the origin (0, 0)? (a) 15 (b) 21 (c) 225 (d) 16
  28. 28.In which quadrant does the point (−8, −6) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  29. 29.In which quadrant does the point (−7, −1) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  30. 30.What is the midpoint of the line joining (6, 3) and (16, 1)? (a) (2, 11) (b) (11, 2) (c) (22, 4) (d) (5, 1)
  31. 31.What is the midpoint of the line joining (3, 6) and (5, 12)? (a) (4, 9) (b) (9, 4) (c) (8, 18) (d) (1, 3)
  32. 32.What is the distance between the points (4, 6) and (8, 9)? (a) 25 (b) 6 (c) 7 (d) 5
  33. 33.In which quadrant does the point (9, 6) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  34. 34.What is the distance between the points (0, 26) and (7, 2)? (a) 26 (b) 625 (c) 25 (d) 31
  35. 35.What is the distance between the points (2, 8) and (10, 14)? (a) 100 (b) 14 (c) 10 (d) 11
  36. 36.What is the distance between the points (1, 1) and (7, 9)? (a) 10 (b) 14 (c) 100 (d) 11
  37. 37.What is the midpoint of the line joining (0, 11) and (2, 5)? (a) (1, 8) (b) (8, 1) (c) (2, 16) (d) (1, 3)
  38. 38.In which quadrant does the point (6, −8) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  39. 39.What is the midpoint of the line joining (0, 6) and (4, 0)? (a) (2, 3) (b) (3, 3) (c) (4, 6) (d) (3, 2)
  40. 40.In which quadrant does the point (−4, −7) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant

Answer key

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

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