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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 392 · 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, 8) and (10, 2)? (a) 11 (b) 100 (c) 10 (d) 14
  2. 2.In which quadrant does the point (−2, −2) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  3. 3.What is the midpoint of the line joining (7, 10) and (19, 20)? (a) (26, 30) (b) (13, 15) (c) (15, 13) (d) (6, 5)
  4. 4.In which quadrant does the point (−7, 2) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  5. 5.In which quadrant does the point (−3, 9) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  6. 6.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 21 (c) 15 (d) 16
  7. 7.What is the distance between the points (9, 7) and (21, 2)? (a) 17 (b) 169 (c) 14 (d) 13
  8. 8.In which quadrant does the point (9, 9) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  9. 9.What is the midpoint of the line joining (4, 8) and (6, 16)? (a) (5, 12) (b) (1, 4) (c) (10, 24) (d) (12, 5)
  10. 10.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 26 (c) 25 (d) 31
  11. 11.What is the midpoint of the line joining (1, 8) and (9, 2)? (a) (6, 5) (b) (10, 10) (c) (5, 5) (d) (4, 3)
  12. 12.What is the distance between the points (1, 8) and (5, 5)? (a) 5 (b) 25 (c) 7 (d) 6
  13. 13.In which quadrant does the point (−3, −1) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  14. 14.What is the distance between the points (4, 6) and (8, 9)? (a) 25 (b) 7 (c) 5 (d) 6
  15. 15.What is the distance between the points (7, 1) and (19, 10)? (a) 16 (b) 15 (c) 21 (d) 225
  16. 16.What is the distance between the points (0, 3) and (3, 7)? (a) 25 (b) 6 (c) 5 (d) 7
  17. 17.What is the distance between the points (0, 13) and (6, 5)? (a) 14 (b) 10 (c) 11 (d) 100
  18. 18.What is the distance between the points (0, 33) and (7, 9)? (a) 26 (b) 625 (c) 31 (d) 25
  19. 19.In which quadrant does the point (−5, −1) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  20. 20.What is the distance between the points (1, 9) and (5, 6)? (a) 6 (b) 7 (c) 5 (d) 25
  21. 21.What is the distance between the points (8, 9) and (12, 12)? (a) 25 (b) 7 (c) 5 (d) 6
  22. 22.What is the distance between the points (3, 6) and (15, 15)? (a) 16 (b) 225 (c) 15 (d) 21
  23. 23.What is the distance between the points (0, 19) and (8, 4)? (a) 23 (b) 18 (c) 289 (d) 17
  24. 24.What is the midpoint of the line joining (4, 9) and (6, 7)? (a) (5, 8) (b) (8, 5) (c) (1, 1) (d) (10, 16)
  25. 25.What is the midpoint of the line joining (9, 14) and (11, 10)? (a) (1, 2) (b) (20, 24) (c) (12, 10) (d) (10, 12)
  26. 26.What is the distance between the points (3, 2) and (15, 11)? (a) 225 (b) 21 (c) 15 (d) 16
  27. 27.What is the midpoint of the line joining (0, 22) and (12, 10)? (a) (6, 6) (b) (16, 6) (c) (12, 32) (d) (6, 16)
  28. 28.What is the distance between the points (1, 9) and (10, 21)? (a) 16 (b) 15 (c) 225 (d) 21
  29. 29.What is the distance between the points (5, 9) and (9, 6)? (a) 25 (b) 7 (c) 6 (d) 5
  30. 30.What is the distance between the points (1, 2) and (7, 10)? (a) 10 (b) 100 (c) 11 (d) 14
  31. 31.In which quadrant does the point (3, −6) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  32. 32.What is the midpoint of the line joining (6, 7) and (16, 11)? (a) (22, 18) (b) (5, 2) (c) (11, 9) (d) (9, 11)
  33. 33.What is the midpoint of the line joining (10, 6) and (16, 10)? (a) (3, 2) (b) (13, 8) (c) (26, 16) (d) (8, 13)
  34. 34.What is the distance between the points (7, 24) and (15, 9)? (a) 23 (b) 289 (c) 18 (d) 17
  35. 35.What is the distance between the points (5, 9) and (17, 0)? (a) 21 (b) 225 (c) 16 (d) 15
  36. 36.What is the distance between the points (6, 3) and (12, 11)? (a) 14 (b) 10 (c) 11 (d) 100
  37. 37.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 169 (c) 13 (d) 17
  38. 38.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 17 (c) 169 (d) 13
  39. 39.In which quadrant does the point (1, 2) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  40. 40.What is the distance between the points (7, 7) and (22, 15)? (a) 289 (b) 23 (c) 18 (d) 17

Answer key

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

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