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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 291 · 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.In which quadrant does the point (−3, 9) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  2. 2.What is the distance between the points (0, 15) and (9, 3)? (a) 21 (b) 15 (c) 16 (d) 225
  3. 3.What is the distance between the points (4, 4) and (13, 16)? (a) 21 (b) 16 (c) 225 (d) 15
  4. 4.What is the distance between the points (4, 11) and (7, 7)? (a) 25 (b) 6 (c) 7 (d) 5
  5. 5.What is the distance between the points (1, 0) and (16, 8)? (a) 289 (b) 23 (c) 18 (d) 17
  6. 6.What is the distance between the points (4, 1) and (7, 5)? (a) 25 (b) 7 (c) 6 (d) 5
  7. 7.What is the distance between the points (2, 15) and (18, 3)? (a) 28 (b) 400 (c) 20 (d) 21
  8. 8.In which quadrant does the point (−2, 4) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  9. 9.What is the distance between the points (3, 0) and (19, 12)? (a) 28 (b) 20 (c) 21 (d) 400
  10. 10.What is the distance between the points (7, 1) and (10, 5)? (a) 6 (b) 5 (c) 7 (d) 25
  11. 11.In which quadrant does the point (−6, −2) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  12. 12.What is the distance between the points (2, 17) and (18, 5)? (a) 21 (b) 400 (c) 20 (d) 28
  13. 13.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 625 (c) 25 (d) 26
  14. 14.What is the midpoint of the line joining (2, 6) and (4, 18)? (a) (6, 24) (b) (3, 12) (c) (12, 3) (d) (1, 6)
  15. 15.What is the distance between the points (4, 12) and (9, 0)? (a) 14 (b) 17 (c) 169 (d) 13
  16. 16.How far is the point (5, 12) from the origin (0, 0)? (a) 13 (b) 17 (c) 169 (d) 14
  17. 17.In which quadrant does the point (−5, −5) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  18. 18.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 625 (c) 25 (d) 26
  19. 19.What is the distance between the points (6, 8) and (14, 23)? (a) 18 (b) 17 (c) 289 (d) 23
  20. 20.What is the distance between the points (5, 13) and (10, 1)? (a) 13 (b) 169 (c) 14 (d) 17
  21. 21.What is the distance between the points (5, 2) and (14, 14)? (a) 21 (b) 225 (c) 15 (d) 16
  22. 22.What is the distance between the points (5, 7) and (13, 13)? (a) 14 (b) 11 (c) 10 (d) 100
  23. 23.In which quadrant does the point (4, −3) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  24. 24.What is the distance between the points (8, 5) and (12, 2)? (a) 25 (b) 7 (c) 6 (d) 5
  25. 25.What is the distance between the points (4, 9) and (19, 17)? (a) 18 (b) 23 (c) 17 (d) 289
  26. 26.What is the distance between the points (3, 6) and (15, 22)? (a) 20 (b) 28 (c) 21 (d) 400
  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.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 11 (c) 10 (d) 100
  29. 29.What is the midpoint of the line joining (2, 5) and (4, 15)? (a) (6, 20) (b) (1, 5) (c) (10, 3) (d) (3, 10)
  30. 30.In which quadrant does the point (−3, 5) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  31. 31.What is the midpoint of the line joining (5, 9) and (17, 11)? (a) (10, 11) (b) (6, 1) (c) (11, 10) (d) (22, 20)
  32. 32.What is the distance between the points (7, 9) and (12, 21)? (a) 13 (b) 169 (c) 17 (d) 14
  33. 33.What is the distance between the points (9, 7) and (25, 19)? (a) 20 (b) 28 (c) 21 (d) 400
  34. 34.What is the distance between the points (2, 2) and (11, 14)? (a) 225 (b) 21 (c) 15 (d) 16
  35. 35.In which quadrant does the point (−8, −7) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  36. 36.What is the midpoint of the line joining (6, 7) and (16, 3)? (a) (11, 5) (b) (5, 11) (c) (22, 10) (d) (5, 2)
  37. 37.What is the distance between the points (6, 1) and (10, 4)? (a) 25 (b) 6 (c) 7 (d) 5
  38. 38.What is the distance between the points (9, 24) and (21, 8)? (a) 400 (b) 20 (c) 28 (d) 21
  39. 39.What is the distance between the points (2, 0) and (9, 24)? (a) 625 (b) 26 (c) 25 (d) 31
  40. 40.In which quadrant does the point (−3, −7) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant

Answer key

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

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