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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 823 · 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 (5, 0) and (8, 4)? (a) 5 (b) 7 (c) 6 (d) 25
  2. 2.What is the midpoint of the line joining (4, 3) and (8, 13)? (a) (12, 16) (b) (8, 6) (c) (6, 8) (d) (2, 5)
  3. 3.In which quadrant does the point (3, 7) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  4. 4.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 23 (c) 18 (d) 17
  5. 5.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 31 (c) 26 (d) 25
  6. 6.How far is the point (16, 12) from the origin (0, 0)? (a) 400 (b) 20 (c) 28 (d) 21
  7. 7.In which quadrant does the point (5, −7) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  8. 8.What is the midpoint of the line joining (2, 2) and (14, 4)? (a) (6, 1) (b) (16, 6) (c) (8, 3) (d) (3, 8)
  9. 9.What is the midpoint of the line joining (3, 9) and (11, 13)? (a) (4, 2) (b) (7, 11) (c) (11, 7) (d) (14, 22)
  10. 10.In which quadrant does the point (2, 7) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  11. 11.What is the distance between the points (2, 1) and (10, 16)? (a) 289 (b) 18 (c) 17 (d) 23
  12. 12.What is the midpoint of the line joining (4, 4) and (8, 10)? (a) (12, 14) (b) (6, 7) (c) (2, 3) (d) (7, 6)
  13. 13.How far is the point (4, 3) from the origin (0, 0)? (a) 5 (b) 6 (c) 25 (d) 7
  14. 14.What is the distance between the points (4, 10) and (16, 1)? (a) 225 (b) 15 (c) 21 (d) 16
  15. 15.In which quadrant does the point (5, −2) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  16. 16.What is the distance between the points (4, 9) and (16, 14)? (a) 14 (b) 169 (c) 13 (d) 17
  17. 17.In which quadrant does the point (−2, −7) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  18. 18.What is the midpoint of the line joining (7, 10) and (11, 14)? (a) (18, 24) (b) (9, 12) (c) (12, 9) (d) (2, 2)
  19. 19.In which quadrant does the point (1, 5) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  20. 20.What is the distance between the points (7, 15) and (15, 0)? (a) 17 (b) 18 (c) 23 (d) 289
  21. 21.What is the distance between the points (3, 10) and (11, 4)? (a) 100 (b) 14 (c) 11 (d) 10
  22. 22.In which quadrant does the point (2, 3) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  23. 23.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 169 (c) 13 (d) 17
  24. 24.What is the midpoint of the line joining (5, 16) and (15, 10)? (a) (13, 10) (b) (20, 26) (c) (5, 3) (d) (10, 13)
  25. 25.What is the midpoint of the line joining (9, 7) and (11, 15)? (a) (11, 10) (b) (10, 11) (c) (20, 22) (d) (1, 4)
  26. 26.What is the midpoint of the line joining (9, 6) and (17, 16)? (a) (26, 22) (b) (13, 11) (c) (11, 13) (d) (4, 5)
  27. 27.In which quadrant does the point (7, 3) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  28. 28.What is the distance between the points (8, 1) and (15, 25)? (a) 25 (b) 31 (c) 26 (d) 625
  29. 29.What is the midpoint of the line joining (1, 0) and (13, 10)? (a) (6, 5) (b) (5, 7) (c) (7, 5) (d) (14, 10)
  30. 30.What is the distance between the points (5, 4) and (14, 16)? (a) 21 (b) 16 (c) 225 (d) 15
  31. 31.What is the distance between the points (7, 5) and (15, 11)? (a) 100 (b) 14 (c) 10 (d) 11
  32. 32.How far is the point (12, 9) from the origin (0, 0)? (a) 16 (b) 15 (c) 225 (d) 21
  33. 33.What is the midpoint of the line joining (8, 1) and (18, 9)? (a) (5, 13) (b) (5, 4) (c) (26, 10) (d) (13, 5)
  34. 34.What is the distance between the points (9, 2) and (18, 14)? (a) 15 (b) 225 (c) 16 (d) 21
  35. 35.What is the distance between the points (1, 4) and (17, 16)? (a) 28 (b) 20 (c) 21 (d) 400
  36. 36.In which quadrant does the point (5, 1) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  37. 37.In which quadrant does the point (−5, 6) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  38. 38.What is the distance between the points (7, 3) and (13, 11)? (a) 10 (b) 14 (c) 100 (d) 11
  39. 39.What is the midpoint of the line joining (1, 4) and (5, 12)? (a) (2, 4) (b) (8, 3) (c) (6, 16) (d) (3, 8)
  40. 40.What is the distance between the points (8, 1) and (20, 10)? (a) 225 (b) 16 (c) 15 (d) 21

Answer key

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

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