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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 500 · 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 (10, 16) and (16, 8)? (a) (3, 4) (b) (26, 24) (c) (13, 12) (d) (12, 13)
  2. 2.What is the distance between the points (1, 17) and (13, 8)? (a) 16 (b) 225 (c) 21 (d) 15
  3. 3.In which quadrant does the point (6, 5) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  4. 4.What is the distance between the points (9, 1) and (12, 5)? (a) 6 (b) 25 (c) 7 (d) 5
  5. 5.In which quadrant does the point (−5, −2) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  6. 6.What is the distance between the points (8, 11) and (16, 5)? (a) 11 (b) 10 (c) 100 (d) 14
  7. 7.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 11 (c) 100 (d) 10
  8. 8.In which quadrant does the point (−2, −6) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  9. 9.What is the distance between the points (1, 6) and (13, 1)? (a) 169 (b) 17 (c) 14 (d) 13
  10. 10.What is the distance between the points (5, 4) and (8, 8)? (a) 25 (b) 7 (c) 6 (d) 5
  11. 11.In which quadrant does the point (4, 9) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  12. 12.What is the distance between the points (5, 4) and (20, 12)? (a) 18 (b) 23 (c) 289 (d) 17
  13. 13.What is the midpoint of the line joining (6, 0) and (12, 12)? (a) (9, 6) (b) (3, 6) (c) (6, 9) (d) (18, 12)
  14. 14.In which quadrant does the point (−3, −9) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  15. 15.What is the distance between the points (1, 9) and (5, 6)? (a) 5 (b) 6 (c) 25 (d) 7
  16. 16.How far is the point (4, 3) from the origin (0, 0)? (a) 5 (b) 25 (c) 6 (d) 7
  17. 17.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 15 (c) 21 (d) 16
  18. 18.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 225 (c) 16 (d) 15
  19. 19.What is the midpoint of the line joining (2, 0) and (12, 8)? (a) (4, 7) (b) (5, 4) (c) (7, 4) (d) (14, 8)
  20. 20.What is the midpoint of the line joining (5, 6) and (13, 14)? (a) (4, 4) (b) (10, 9) (c) (18, 20) (d) (9, 10)
  21. 21.What is the distance between the points (4, 8) and (12, 14)? (a) 14 (b) 10 (c) 100 (d) 11
  22. 22.In which quadrant does the point (−8, −2) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  23. 23.What is the midpoint of the line joining (0, 3) and (12, 9)? (a) (12, 12) (b) (6, 6) (c) (6, 3) (d) (7, 6)
  24. 24.What is the midpoint of the line joining (4, 9) and (12, 5)? (a) (4, 2) (b) (16, 14) (c) (8, 7) (d) (7, 8)
  25. 25.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 18 (c) 17 (d) 289
  26. 26.What is the midpoint of the line joining (6, 3) and (18, 15)? (a) (9, 12) (b) (6, 6) (c) (24, 18) (d) (12, 9)
  27. 27.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 400 (c) 28 (d) 20
  28. 28.What is the midpoint of the line joining (2, 6) and (10, 8)? (a) (6, 7) (b) (12, 14) (c) (7, 6) (d) (4, 1)
  29. 29.What is the distance between the points (8, 15) and (16, 9)? (a) 10 (b) 14 (c) 11 (d) 100
  30. 30.How far is the point (15, 8) from the origin (0, 0)? (a) 17 (b) 18 (c) 23 (d) 289
  31. 31.What is the distance between the points (9, 11) and (17, 5)? (a) 10 (b) 100 (c) 11 (d) 14
  32. 32.What is the distance between the points (3, 6) and (27, 13)? (a) 25 (b) 625 (c) 31 (d) 26
  33. 33.What is the midpoint of the line joining (10, 9) and (12, 19)? (a) (11, 14) (b) (22, 28) (c) (1, 5) (d) (14, 11)
  34. 34.In which quadrant does the point (6, −5) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  35. 35.What is the midpoint of the line joining (8, 19) and (10, 7)? (a) (1, 6) (b) (9, 13) (c) (18, 26) (d) (13, 9)
  36. 36.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 10 (c) 11 (d) 100
  37. 37.In which quadrant does the point (−7, −7) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  38. 38.In which quadrant does the point (3, 4) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  39. 39.In which quadrant does the point (2, −8) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  40. 40.What is the midpoint of the line joining (10, 9) and (12, 13)? (a) (12, 11) (b) (11, 11) (c) (22, 22) (d) (1, 2)

Answer key

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

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