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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 487 · 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, 5) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  2. 2.What is the midpoint of the line joining (10, 18) and (20, 10)? (a) (14, 15) (b) (30, 28) (c) (5, 4) (d) (15, 14)
  3. 3.What is the midpoint of the line joining (6, 10) and (8, 6)? (a) (1, 2) (b) (8, 7) (c) (14, 16) (d) (7, 8)
  4. 4.What is the distance between the points (1, 19) and (6, 7)? (a) 17 (b) 13 (c) 169 (d) 14
  5. 5.What is the midpoint of the line joining (8, 6) and (14, 10)? (a) (3, 2) (b) (11, 8) (c) (22, 16) (d) (8, 11)
  6. 6.In which quadrant does the point (−6, −6) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  7. 7.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 18 (c) 23 (d) 17
  8. 8.What is the midpoint of the line joining (6, 7) and (16, 19)? (a) (22, 26) (b) (13, 11) (c) (11, 13) (d) (5, 6)
  9. 9.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 17 (c) 13 (d) 14
  10. 10.What is the distance between the points (2, 10) and (5, 6)? (a) 7 (b) 25 (c) 5 (d) 6
  11. 11.In which quadrant does the point (−2, 8) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  12. 12.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 10 (c) 100 (d) 14
  13. 13.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 11 (c) 10 (d) 100
  14. 14.In which quadrant does the point (8, −7) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  15. 15.What is the distance between the points (8, 9) and (14, 1)? (a) 11 (b) 10 (c) 14 (d) 100
  16. 16.What is the distance between the points (7, 11) and (31, 4)? (a) 25 (b) 625 (c) 31 (d) 26
  17. 17.In which quadrant does the point (6, 2) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  18. 18.How far is the point (24, 7) from the origin (0, 0)? (a) 25 (b) 26 (c) 625 (d) 31
  19. 19.What is the distance between the points (3, 1) and (7, 4)? (a) 7 (b) 5 (c) 6 (d) 25
  20. 20.What is the distance between the points (9, 6) and (21, 1)? (a) 17 (b) 14 (c) 169 (d) 13
  21. 21.In which quadrant does the point (5, 1) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  22. 22.What is the midpoint of the line joining (2, 6) and (6, 10)? (a) (8, 16) (b) (2, 2) (c) (4, 8) (d) (8, 4)
  23. 23.In which quadrant does the point (−1, 7) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  24. 24.What is the midpoint of the line joining (1, 9) and (11, 17)? (a) (13, 6) (b) (12, 26) (c) (5, 4) (d) (6, 13)
  25. 25.What is the distance between the points (5, 12) and (9, 9)? (a) 7 (b) 6 (c) 25 (d) 5
  26. 26.What is the distance between the points (8, 1) and (12, 4)? (a) 7 (b) 25 (c) 5 (d) 6
  27. 27.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 21 (c) 20 (d) 400
  28. 28.What is the distance between the points (0, 3) and (12, 12)? (a) 225 (b) 21 (c) 16 (d) 15
  29. 29.In which quadrant does the point (1, 2) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  30. 30.In which quadrant does the point (8, 3) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  31. 31.What is the distance between the points (4, 1) and (11, 25)? (a) 31 (b) 25 (c) 26 (d) 625
  32. 32.What is the distance between the points (2, 9) and (14, 25)? (a) 28 (b) 20 (c) 400 (d) 21
  33. 33.What is the distance between the points (1, 20) and (17, 8)? (a) 400 (b) 21 (c) 28 (d) 20
  34. 34.In which quadrant does the point (8, −2) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  35. 35.What is the midpoint of the line joining (6, 8) and (10, 6)? (a) (7, 8) (b) (8, 7) (c) (16, 14) (d) (2, 1)
  36. 36.What is the midpoint of the line joining (3, 4) and (11, 2)? (a) (4, 1) (b) (3, 7) (c) (14, 6) (d) (7, 3)
  37. 37.What is the midpoint of the line joining (7, 3) and (15, 5)? (a) (22, 8) (b) (4, 11) (c) (4, 1) (d) (11, 4)
  38. 38.What is the distance between the points (5, 22) and (17, 6)? (a) 21 (b) 400 (c) 28 (d) 20
  39. 39.What is the distance between the points (8, 8) and (23, 0)? (a) 289 (b) 17 (c) 23 (d) 18
  40. 40.In which quadrant does the point (4, 5) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant

Answer key

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

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