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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 146 · 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, 12) and (5, 2)? (a) (2, 5) (b) (7, 3) (c) (3, 7) (d) (6, 14)
  2. 2.In which quadrant does the point (7, −4) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  3. 3.What is the distance between the points (7, 7) and (19, 23)? (a) 400 (b) 20 (c) 28 (d) 21
  4. 4.What is the distance between the points (6, 9) and (10, 6)? (a) 7 (b) 5 (c) 6 (d) 25
  5. 5.What is the distance between the points (0, 32) and (7, 8)? (a) 625 (b) 26 (c) 25 (d) 31
  6. 6.In which quadrant does the point (−4, −5) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  7. 7.What is the midpoint of the line joining (8, 3) and (18, 9)? (a) (6, 13) (b) (5, 3) (c) (26, 12) (d) (13, 6)
  8. 8.What is the distance between the points (5, 1) and (8, 5)? (a) 5 (b) 7 (c) 6 (d) 25
  9. 9.What is the distance between the points (6, 17) and (14, 2)? (a) 17 (b) 289 (c) 18 (d) 23
  10. 10.What is the midpoint of the line joining (6, 12) and (8, 6)? (a) (7, 9) (b) (1, 3) (c) (14, 18) (d) (9, 7)
  11. 11.In which quadrant does the point (−6, −5) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  12. 12.In which quadrant does the point (6, −8) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  13. 13.What is the midpoint of the line joining (6, 8) and (14, 6)? (a) (4, 1) (b) (20, 14) (c) (10, 7) (d) (7, 10)
  14. 14.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 13 (c) 14 (d) 17
  15. 15.In which quadrant does the point (8, 9) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  16. 16.What is the midpoint of the line joining (1, 10) and (5, 12)? (a) (2, 1) (b) (3, 11) (c) (6, 22) (d) (11, 3)
  17. 17.What is the distance between the points (0, 1) and (7, 25)? (a) 31 (b) 25 (c) 26 (d) 625
  18. 18.What is the distance between the points (6, 14) and (30, 7)? (a) 31 (b) 625 (c) 25 (d) 26
  19. 19.What is the distance between the points (8, 4) and (11, 0)? (a) 5 (b) 6 (c) 7 (d) 25
  20. 20.What is the distance between the points (2, 8) and (10, 14)? (a) 11 (b) 14 (c) 100 (d) 10
  21. 21.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 100 (c) 10 (d) 11
  22. 22.How far is the point (16, 12) from the origin (0, 0)? (a) 400 (b) 20 (c) 21 (d) 28
  23. 23.What is the distance between the points (5, 3) and (14, 15)? (a) 15 (b) 16 (c) 225 (d) 21
  24. 24.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 7 (c) 5 (d) 25
  25. 25.How far is the point (12, 9) from the origin (0, 0)? (a) 16 (b) 15 (c) 21 (d) 225
  26. 26.What is the distance between the points (3, 8) and (11, 14)? (a) 11 (b) 10 (c) 100 (d) 14
  27. 27.What is the midpoint of the line joining (10, 4) and (20, 16)? (a) (15, 10) (b) (10, 15) (c) (30, 20) (d) (5, 6)
  28. 28.In which quadrant does the point (3, −6) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  29. 29.In which quadrant does the point (7, 2) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  30. 30.In which quadrant does the point (−1, 9) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  31. 31.What is the distance between the points (7, 4) and (19, 20)? (a) 400 (b) 20 (c) 21 (d) 28
  32. 32.What is the distance between the points (0, 0) and (12, 5)? (a) 169 (b) 17 (c) 14 (d) 13
  33. 33.In which quadrant does the point (4, −4) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  34. 34.What is the distance between the points (0, 9) and (3, 13)? (a) 7 (b) 6 (c) 25 (d) 5
  35. 35.What is the midpoint of the line joining (9, 10) and (21, 14)? (a) (30, 24) (b) (12, 15) (c) (15, 12) (d) (6, 2)
  36. 36.In which quadrant does the point (8, 6) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  37. 37.What is the midpoint of the line joining (4, 3) and (8, 13)? (a) (6, 8) (b) (2, 5) (c) (8, 6) (d) (12, 16)
  38. 38.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 26 (c) 625 (d) 25
  39. 39.What is the distance between the points (1, 9) and (17, 21)? (a) 400 (b) 28 (c) 21 (d) 20
  40. 40.What is the midpoint of the line joining (7, 8) and (17, 10)? (a) (24, 18) (b) (12, 9) (c) (5, 1) (d) (9, 12)

Answer key

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

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