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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 650 · 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 (7, 8) and (11, 11)? (a) 7 (b) 6 (c) 25 (d) 5
  2. 2.What is the distance between the points (4, 13) and (19, 5)? (a) 17 (b) 23 (c) 289 (d) 18
  3. 3.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 28 (c) 400 (d) 20
  4. 4.What is the distance between the points (9, 22) and (21, 6)? (a) 21 (b) 28 (c) 400 (d) 20
  5. 5.In which quadrant does the point (8, 6) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  6. 6.In which quadrant does the point (−8, 1) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  7. 7.What is the midpoint of the line joining (7, 8) and (19, 18)? (a) (13, 13) (b) (6, 5) (c) (14, 13) (d) (26, 26)
  8. 8.What is the midpoint of the line joining (1, 14) and (9, 8)? (a) (4, 3) (b) (10, 22) (c) (11, 5) (d) (5, 11)
  9. 9.What is the midpoint of the line joining (8, 9) and (20, 1)? (a) (5, 14) (b) (28, 10) (c) (6, 4) (d) (14, 5)
  10. 10.In which quadrant does the point (9, −5) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  11. 11.In which quadrant does the point (7, −2) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  12. 12.What is the distance between the points (2, 31) and (9, 7)? (a) 31 (b) 625 (c) 25 (d) 26
  13. 13.What is the midpoint of the line joining (8, 0) and (20, 10)? (a) (28, 10) (b) (5, 14) (c) (6, 5) (d) (14, 5)
  14. 14.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 17 (c) 289 (d) 23
  15. 15.What is the distance between the points (7, 20) and (19, 4)? (a) 28 (b) 20 (c) 21 (d) 400
  16. 16.What is the midpoint of the line joining (9, 13) and (15, 7)? (a) (12, 10) (b) (3, 3) (c) (24, 20) (d) (10, 12)
  17. 17.What is the midpoint of the line joining (4, 13) and (16, 1)? (a) (6, 6) (b) (10, 7) (c) (20, 14) (d) (7, 10)
  18. 18.In which quadrant does the point (9, 4) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  19. 19.What is the midpoint of the line joining (4, 5) and (8, 9)? (a) (2, 2) (b) (6, 7) (c) (7, 6) (d) (12, 14)
  20. 20.What is the midpoint of the line joining (5, 16) and (17, 8)? (a) (6, 4) (b) (22, 24) (c) (11, 12) (d) (12, 11)
  21. 21.What is the distance between the points (2, 1) and (10, 16)? (a) 289 (b) 23 (c) 18 (d) 17
  22. 22.What is the distance between the points (0, 3) and (8, 9)? (a) 10 (b) 11 (c) 100 (d) 14
  23. 23.What is the distance between the points (7, 9) and (11, 6)? (a) 7 (b) 6 (c) 5 (d) 25
  24. 24.What is the midpoint of the line joining (8, 7) and (20, 5)? (a) (14, 6) (b) (6, 14) (c) (28, 12) (d) (6, 1)
  25. 25.What is the distance between the points (9, 21) and (18, 9)? (a) 225 (b) 21 (c) 15 (d) 16
  26. 26.What is the midpoint of the line joining (7, 7) and (11, 19)? (a) (13, 9) (b) (9, 13) (c) (18, 26) (d) (2, 6)
  27. 27.What is the distance between the points (8, 6) and (20, 11)? (a) 17 (b) 14 (c) 13 (d) 169
  28. 28.What is the distance between the points (1, 11) and (4, 7)? (a) 7 (b) 6 (c) 25 (d) 5
  29. 29.What is the distance between the points (5, 15) and (13, 0)? (a) 23 (b) 17 (c) 289 (d) 18
  30. 30.In which quadrant does the point (−8, 4) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  31. 31.In which quadrant does the point (4, 9) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  32. 32.In which quadrant does the point (−1, 5) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  33. 33.In which quadrant does the point (2, 4) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  34. 34.What is the midpoint of the line joining (5, 9) and (15, 21)? (a) (15, 10) (b) (5, 6) (c) (10, 15) (d) (20, 30)
  35. 35.In which quadrant does the point (−6, −5) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  36. 36.In which quadrant does the point (8, 5) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  37. 37.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 225 (c) 16 (d) 15
  38. 38.What is the midpoint of the line joining (4, 5) and (16, 9)? (a) (10, 7) (b) (6, 2) (c) (20, 14) (d) (7, 10)
  39. 39.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 7 (c) 6 (d) 5
  40. 40.What is the midpoint of the line joining (2, 4) and (4, 6)? (a) (6, 10) (b) (5, 3) (c) (1, 1) (d) (3, 5)

Answer key

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

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