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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 437 · 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 (8, 1) and (10, 3)? (a) (9, 2) (b) (18, 4) (c) (1, 1) (d) (2, 9)
  2. 2.In which quadrant does the point (−1, −1) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  3. 3.In which quadrant does the point (1, 4) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  4. 4.What is the midpoint of the line joining (7, 0) and (19, 6)? (a) (13, 3) (b) (6, 3) (c) (3, 13) (d) (26, 6)
  5. 5.How far is the point (12, 9) from the origin (0, 0)? (a) 16 (b) 225 (c) 15 (d) 21
  6. 6.In which quadrant does the point (−2, 7) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  7. 7.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 400 (c) 20 (d) 21
  8. 8.In which quadrant does the point (−9, −3) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  9. 9.In which quadrant does the point (−1, 8) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  10. 10.What is the midpoint of the line joining (2, 3) and (4, 9)? (a) (1, 3) (b) (6, 12) (c) (6, 3) (d) (3, 6)
  11. 11.What is the midpoint of the line joining (0, 2) and (2, 10)? (a) (6, 1) (b) (2, 12) (c) (1, 6) (d) (1, 4)
  12. 12.In which quadrant does the point (2, −6) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  13. 13.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 25 (c) 5 (d) 6
  14. 14.In which quadrant does the point (−5, 7) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  15. 15.In which quadrant does the point (−3, −1) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  16. 16.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 100 (c) 10 (d) 11
  17. 17.What is the midpoint of the line joining (5, 7) and (7, 11)? (a) (9, 6) (b) (12, 18) (c) (6, 9) (d) (1, 2)
  18. 18.What is the distance between the points (2, 7) and (6, 4)? (a) 25 (b) 7 (c) 6 (d) 5
  19. 19.In which quadrant does the point (1, 2) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  20. 20.In which quadrant does the point (−9, −6) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  21. 21.In which quadrant does the point (9, −8) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  22. 22.What is the distance between the points (7, 1) and (19, 17)? (a) 20 (b) 21 (c) 28 (d) 400
  23. 23.What is the distance between the points (8, 8) and (24, 20)? (a) 21 (b) 400 (c) 20 (d) 28
  24. 24.In which quadrant does the point (8, 7) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  25. 25.What is the distance between the points (4, 8) and (12, 2)? (a) 10 (b) 100 (c) 11 (d) 14
  26. 26.What is the midpoint of the line joining (8, 11) and (18, 7)? (a) (9, 13) (b) (26, 18) (c) (5, 2) (d) (13, 9)
  27. 27.What is the midpoint of the line joining (6, 14) and (12, 6)? (a) (10, 9) (b) (9, 10) (c) (18, 20) (d) (3, 4)
  28. 28.In which quadrant does the point (1, 5) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  29. 29.What is the distance between the points (9, 31) and (16, 7)? (a) 31 (b) 26 (c) 625 (d) 25
  30. 30.What is the distance between the points (6, 7) and (14, 22)? (a) 18 (b) 23 (c) 17 (d) 289
  31. 31.What is the midpoint of the line joining (0, 3) and (2, 5)? (a) (2, 8) (b) (4, 1) (c) (1, 1) (d) (1, 4)
  32. 32.In which quadrant does the point (7, 7) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  33. 33.What is the distance between the points (9, 6) and (24, 14)? (a) 289 (b) 23 (c) 18 (d) 17
  34. 34.What is the distance between the points (3, 13) and (15, 8)? (a) 169 (b) 14 (c) 17 (d) 13
  35. 35.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 17 (c) 13 (d) 14
  36. 36.What is the midpoint of the line joining (10, 1) and (14, 9)? (a) (2, 4) (b) (12, 5) (c) (5, 12) (d) (24, 10)
  37. 37.What is the midpoint of the line joining (5, 2) and (17, 12)? (a) (7, 11) (b) (11, 7) (c) (22, 14) (d) (6, 5)
  38. 38.What is the midpoint of the line joining (0, 4) and (10, 6)? (a) (5, 5) (b) (10, 10) (c) (5, 1) (d) (6, 5)
  39. 39.In which quadrant does the point (2, 1) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  40. 40.What is the distance between the points (7, 9) and (15, 15)? (a) 11 (b) 100 (c) 10 (d) 14

Answer key

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

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