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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 666 · 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 (7, 8) and (19, 10)? (a) (9, 13) (b) (26, 18) (c) (6, 1) (d) (13, 9)
  2. 2.What is the distance between the points (1, 17) and (17, 5)? (a) 400 (b) 28 (c) 21 (d) 20
  3. 3.In which quadrant does the point (−1, 9) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  4. 4.In which quadrant does the point (3, 7) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  5. 5.What is the distance between the points (6, 6) and (9, 10)? (a) 6 (b) 7 (c) 25 (d) 5
  6. 6.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 625 (c) 31 (d) 25
  7. 7.What is the midpoint of the line joining (3, 10) and (7, 14)? (a) (12, 5) (b) (2, 2) (c) (10, 24) (d) (5, 12)
  8. 8.What is the distance between the points (3, 17) and (8, 5)? (a) 169 (b) 17 (c) 13 (d) 14
  9. 9.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 17 (c) 18 (d) 23
  10. 10.What is the midpoint of the line joining (1, 2) and (13, 14)? (a) (14, 16) (b) (8, 7) (c) (7, 8) (d) (6, 6)
  11. 11.What is the midpoint of the line joining (7, 6) and (19, 12)? (a) (26, 18) (b) (9, 13) (c) (6, 3) (d) (13, 9)
  12. 12.What is the midpoint of the line joining (7, 11) and (19, 3)? (a) (7, 13) (b) (26, 14) (c) (13, 7) (d) (6, 4)
  13. 13.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 7 (c) 5 (d) 25
  14. 14.In which quadrant does the point (−2, 3) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  15. 15.What is the distance between the points (2, 3) and (17, 11)? (a) 289 (b) 18 (c) 17 (d) 23
  16. 16.What is the midpoint of the line joining (9, 6) and (13, 10)? (a) (2, 2) (b) (8, 11) (c) (11, 8) (d) (22, 16)
  17. 17.What is the distance between the points (1, 1) and (4, 5)? (a) 7 (b) 25 (c) 6 (d) 5
  18. 18.In which quadrant does the point (−6, −8) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  19. 19.In which quadrant does the point (8, 9) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  20. 20.What is the midpoint of the line joining (6, 11) and (14, 1)? (a) (6, 10) (b) (20, 12) (c) (10, 6) (d) (4, 5)
  21. 21.What is the distance between the points (9, 2) and (21, 11)? (a) 225 (b) 15 (c) 21 (d) 16
  22. 22.What is the distance between the points (3, 1) and (11, 16)? (a) 17 (b) 18 (c) 23 (d) 289
  23. 23.What is the distance between the points (7, 3) and (11, 6)? (a) 6 (b) 5 (c) 25 (d) 7
  24. 24.In which quadrant does the point (8, −1) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  25. 25.What is the distance between the points (4, 1) and (20, 13)? (a) 20 (b) 400 (c) 28 (d) 21
  26. 26.In which quadrant does the point (−5, −7) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  27. 27.In which quadrant does the point (2, −4) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  28. 28.What is the midpoint of the line joining (3, 3) and (13, 1)? (a) (2, 8) (b) (8, 2) (c) (16, 4) (d) (5, 1)
  29. 29.What is the midpoint of the line joining (9, 4) and (21, 0)? (a) (2, 15) (b) (6, 2) (c) (30, 4) (d) (15, 2)
  30. 30.What is the distance between the points (4, 0) and (16, 16)? (a) 21 (b) 400 (c) 20 (d) 28
  31. 31.What is the distance between the points (7, 1) and (12, 13)? (a) 13 (b) 17 (c) 14 (d) 169
  32. 32.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 21 (c) 16 (d) 15
  33. 33.What is the distance between the points (0, 6) and (8, 0)? (a) 11 (b) 10 (c) 100 (d) 14
  34. 34.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 16 (c) 15 (d) 225
  35. 35.What is the midpoint of the line joining (9, 9) and (17, 1)? (a) (13, 5) (b) (26, 10) (c) (4, 4) (d) (5, 13)
  36. 36.In which quadrant does the point (−7, −2) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  37. 37.What is the distance between the points (4, 6) and (12, 12)? (a) 11 (b) 14 (c) 100 (d) 10
  38. 38.What is the distance between the points (9, 9) and (24, 17)? (a) 18 (b) 289 (c) 23 (d) 17
  39. 39.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 11 (c) 14 (d) 10
  40. 40.What is the distance between the points (9, 24) and (16, 0)? (a) 625 (b) 25 (c) 26 (d) 31

Answer key

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

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