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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 587 · 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 (2, 9) and (26, 16)? (a) 25 (b) 31 (c) 625 (d) 26
  2. 2.What is the midpoint of the line joining (8, 1) and (14, 11)? (a) (6, 11) (b) (11, 6) (c) (3, 5) (d) (22, 12)
  3. 3.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 7 (c) 6 (d) 25
  4. 4.What is the midpoint of the line joining (1, 9) and (3, 17)? (a) (2, 13) (b) (13, 2) (c) (4, 26) (d) (1, 4)
  5. 5.What is the distance between the points (8, 15) and (16, 0)? (a) 17 (b) 289 (c) 23 (d) 18
  6. 6.What is the midpoint of the line joining (2, 8) and (12, 20)? (a) (7, 14) (b) (14, 7) (c) (14, 28) (d) (5, 6)
  7. 7.What is the distance between the points (4, 2) and (19, 10)? (a) 17 (b) 23 (c) 18 (d) 289
  8. 8.In which quadrant does the point (−7, 4) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  9. 9.What is the midpoint of the line joining (4, 13) and (14, 3)? (a) (9, 8) (b) (18, 16) (c) (5, 5) (d) (8, 9)
  10. 10.What is the midpoint of the line joining (0, 2) and (12, 14)? (a) (6, 6) (b) (6, 8) (c) (8, 6) (d) (12, 16)
  11. 11.What is the distance between the points (0, 6) and (24, 13)? (a) 25 (b) 31 (c) 625 (d) 26
  12. 12.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 400 (c) 20 (d) 28
  13. 13.What is the midpoint of the line joining (9, 13) and (17, 3)? (a) (4, 5) (b) (13, 8) (c) (8, 13) (d) (26, 16)
  14. 14.What is the distance between the points (4, 13) and (10, 5)? (a) 11 (b) 100 (c) 10 (d) 14
  15. 15.What is the distance between the points (6, 11) and (30, 4)? (a) 625 (b) 26 (c) 31 (d) 25
  16. 16.In which quadrant does the point (4, −6) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  17. 17.How far is the point (7, 24) from the origin (0, 0)? (a) 25 (b) 26 (c) 625 (d) 31
  18. 18.In which quadrant does the point (5, 9) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  19. 19.What is the distance between the points (7, 12) and (19, 3)? (a) 16 (b) 225 (c) 15 (d) 21
  20. 20.In which quadrant does the point (1, 1) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  21. 21.What is the distance between the points (4, 14) and (10, 6)? (a) 100 (b) 14 (c) 11 (d) 10
  22. 22.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 10 (c) 100 (d) 11
  23. 23.What is the midpoint of the line joining (9, 7) and (15, 19)? (a) (3, 6) (b) (13, 12) (c) (24, 26) (d) (12, 13)
  24. 24.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 289 (c) 18 (d) 17
  25. 25.What is the midpoint of the line joining (0, 6) and (8, 14)? (a) (10, 4) (b) (4, 4) (c) (8, 20) (d) (4, 10)
  26. 26.What is the distance between the points (9, 1) and (21, 17)? (a) 21 (b) 400 (c) 28 (d) 20
  27. 27.What is the midpoint of the line joining (10, 12) and (16, 6)? (a) (9, 13) (b) (13, 9) (c) (3, 3) (d) (26, 18)
  28. 28.In which quadrant does the point (2, −1) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  29. 29.What is the midpoint of the line joining (0, 6) and (4, 0)? (a) (2, 3) (b) (3, 2) (c) (3, 3) (d) (4, 6)
  30. 30.In which quadrant does the point (−4, −3) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  31. 31.What is the distance between the points (2, 11) and (10, 5)? (a) 10 (b) 14 (c) 100 (d) 11
  32. 32.What is the distance between the points (9, 4) and (12, 8)? (a) 7 (b) 6 (c) 25 (d) 5
  33. 33.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 100 (c) 14 (d) 10
  34. 34.What is the midpoint of the line joining (1, 12) and (3, 8)? (a) (1, 2) (b) (10, 2) (c) (2, 10) (d) (4, 20)
  35. 35.In which quadrant does the point (7, 5) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  36. 36.What is the distance between the points (5, 12) and (8, 8)? (a) 7 (b) 25 (c) 6 (d) 5
  37. 37.What is the midpoint of the line joining (3, 8) and (5, 2)? (a) (5, 4) (b) (8, 10) (c) (1, 3) (d) (4, 5)
  38. 38.What is the distance between the points (7, 5) and (10, 9)? (a) 7 (b) 25 (c) 6 (d) 5
  39. 39.What is the distance between the points (5, 5) and (8, 1)? (a) 25 (b) 5 (c) 7 (d) 6
  40. 40.What is the distance between the points (1, 8) and (13, 3)? (a) 169 (b) 13 (c) 17 (d) 14

Answer key

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

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