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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 398 · 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, 6) and (10, 21)? (a) 18 (b) 289 (c) 23 (d) 17
  2. 2.How far is the point (7, 24) from the origin (0, 0)? (a) 25 (b) 26 (c) 625 (d) 31
  3. 3.In which quadrant does the point (4, −3) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  4. 4.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 5 (c) 7 (d) 6
  5. 5.What is the distance between the points (7, 6) and (16, 18)? (a) 15 (b) 225 (c) 16 (d) 21
  6. 6.What is the distance between the points (7, 6) and (19, 1)? (a) 169 (b) 14 (c) 17 (d) 13
  7. 7.In which quadrant does the point (9, −2) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  8. 8.What is the midpoint of the line joining (8, 10) and (12, 12)? (a) (11, 10) (b) (2, 1) (c) (20, 22) (d) (10, 11)
  9. 9.How far is the point (12, 5) from the origin (0, 0)? (a) 13 (b) 17 (c) 14 (d) 169
  10. 10.What is the distance between the points (7, 10) and (15, 4)? (a) 100 (b) 10 (c) 14 (d) 11
  11. 11.In which quadrant does the point (1, 8) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  12. 12.What is the distance between the points (0, 7) and (12, 16)? (a) 16 (b) 225 (c) 15 (d) 21
  13. 13.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 289 (c) 17 (d) 18
  14. 14.What is the midpoint of the line joining (7, 3) and (13, 13)? (a) (20, 16) (b) (8, 10) (c) (3, 5) (d) (10, 8)
  15. 15.In which quadrant does the point (4, 3) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  16. 16.What is the distance between the points (6, 16) and (18, 0)? (a) 28 (b) 400 (c) 20 (d) 21
  17. 17.What is the distance between the points (1, 14) and (17, 2)? (a) 21 (b) 28 (c) 20 (d) 400
  18. 18.In which quadrant does the point (−3, −6) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  19. 19.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 17 (c) 13 (d) 169
  20. 20.What is the distance between the points (9, 3) and (24, 11)? (a) 289 (b) 18 (c) 23 (d) 17
  21. 21.What is the distance between the points (8, 11) and (16, 5)? (a) 10 (b) 100 (c) 14 (d) 11
  22. 22.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 100 (c) 11 (d) 14
  23. 23.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 225 (c) 21 (d) 15
  24. 24.In which quadrant does the point (9, 9) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  25. 25.In which quadrant does the point (−4, −1) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  26. 26.What is the distance between the points (3, 6) and (12, 18)? (a) 21 (b) 15 (c) 225 (d) 16
  27. 27.What is the midpoint of the line joining (10, 2) and (14, 8)? (a) (5, 12) (b) (2, 3) (c) (24, 10) (d) (12, 5)
  28. 28.What is the distance between the points (2, 15) and (26, 8)? (a) 25 (b) 625 (c) 31 (d) 26
  29. 29.What is the midpoint of the line joining (7, 5) and (17, 11)? (a) (8, 12) (b) (5, 3) (c) (24, 16) (d) (12, 8)
  30. 30.What is the midpoint of the line joining (2, 9) and (6, 21)? (a) (2, 6) (b) (8, 30) (c) (15, 4) (d) (4, 15)
  31. 31.What is the midpoint of the line joining (10, 15) and (22, 5)? (a) (10, 16) (b) (6, 5) (c) (16, 10) (d) (32, 20)
  32. 32.What is the distance between the points (0, 2) and (12, 18)? (a) 21 (b) 20 (c) 400 (d) 28
  33. 33.In which quadrant does the point (6, −5) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  34. 34.What is the midpoint of the line joining (9, 3) and (15, 5)? (a) (4, 12) (b) (24, 8) (c) (12, 4) (d) (3, 1)
  35. 35.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 28 (c) 400 (d) 20
  36. 36.What is the distance between the points (1, 6) and (13, 1)? (a) 14 (b) 13 (c) 17 (d) 169
  37. 37.What is the distance between the points (8, 14) and (24, 2)? (a) 28 (b) 21 (c) 20 (d) 400
  38. 38.In which quadrant does the point (5, −4) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  39. 39.In which quadrant does the point (−2, 1) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  40. 40.In which quadrant does the point (−6, 4) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant

Answer key

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

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