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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 194 · 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 (6, 5) and (10, 8)? (a) 7 (b) 6 (c) 5 (d) 25
  2. 2.In which quadrant does the point (−4, −8) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  3. 3.In which quadrant does the point (−2, 8) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  4. 4.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 7 (c) 6 (d) 5
  5. 5.What is the distance between the points (5, 25) and (17, 9)? (a) 20 (b) 400 (c) 28 (d) 21
  6. 6.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 14 (c) 11 (d) 100
  7. 7.What is the distance between the points (5, 9) and (17, 14)? (a) 13 (b) 169 (c) 17 (d) 14
  8. 8.In which quadrant does the point (6, 5) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  9. 9.What is the distance between the points (9, 3) and (18, 15)? (a) 16 (b) 15 (c) 21 (d) 225
  10. 10.What is the distance between the points (3, 21) and (11, 6)? (a) 289 (b) 17 (c) 23 (d) 18
  11. 11.What is the distance between the points (3, 8) and (12, 20)? (a) 16 (b) 225 (c) 15 (d) 21
  12. 12.What is the distance between the points (9, 0) and (33, 7)? (a) 625 (b) 26 (c) 25 (d) 31
  13. 13.What is the distance between the points (0, 5) and (15, 13)? (a) 18 (b) 17 (c) 289 (d) 23
  14. 14.How far is the point (15, 8) from the origin (0, 0)? (a) 17 (b) 18 (c) 289 (d) 23
  15. 15.In which quadrant does the point (−1, −7) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  16. 16.What is the distance between the points (0, 1) and (9, 13)? (a) 15 (b) 21 (c) 16 (d) 225
  17. 17.How far is the point (9, 12) from the origin (0, 0)? (a) 15 (b) 21 (c) 16 (d) 225
  18. 18.What is the distance between the points (0, 3) and (6, 11)? (a) 11 (b) 100 (c) 10 (d) 14
  19. 19.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 21 (c) 400 (d) 20
  20. 20.What is the midpoint of the line joining (4, 17) and (14, 7)? (a) (9, 12) (b) (5, 5) (c) (18, 24) (d) (12, 9)
  21. 21.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 169 (c) 13 (d) 17
  22. 22.What is the midpoint of the line joining (0, 8) and (8, 10)? (a) (8, 18) (b) (4, 9) (c) (9, 4) (d) (4, 1)
  23. 23.In which quadrant does the point (−2, 1) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  24. 24.What is the distance between the points (1, 0) and (6, 12)? (a) 17 (b) 169 (c) 14 (d) 13
  25. 25.What is the midpoint of the line joining (10, 16) and (12, 10)? (a) (1, 3) (b) (13, 11) (c) (11, 13) (d) (22, 26)
  26. 26.What is the midpoint of the line joining (2, 15) and (6, 5)? (a) (8, 20) (b) (10, 4) (c) (2, 5) (d) (4, 10)
  27. 27.What is the midpoint of the line joining (8, 8) and (18, 14)? (a) (11, 13) (b) (13, 11) (c) (26, 22) (d) (5, 3)
  28. 28.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 625 (c) 25 (d) 31
  29. 29.In which quadrant does the point (7, −2) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  30. 30.What is the distance between the points (5, 4) and (29, 11)? (a) 26 (b) 625 (c) 25 (d) 31
  31. 31.What is the distance between the points (3, 25) and (10, 1)? (a) 26 (b) 25 (c) 625 (d) 31
  32. 32.What is the midpoint of the line joining (2, 5) and (10, 1)? (a) (3, 6) (b) (12, 6) (c) (4, 2) (d) (6, 3)
  33. 33.In which quadrant does the point (6, 9) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  34. 34.What is the distance between the points (3, 10) and (6, 6)? (a) 7 (b) 25 (c) 5 (d) 6
  35. 35.What is the midpoint of the line joining (0, 6) and (4, 14)? (a) (4, 20) (b) (2, 10) (c) (2, 4) (d) (10, 2)
  36. 36.What is the distance between the points (9, 8) and (13, 11)? (a) 25 (b) 7 (c) 6 (d) 5
  37. 37.What is the distance between the points (5, 2) and (9, 5)? (a) 6 (b) 5 (c) 7 (d) 25
  38. 38.What is the midpoint of the line joining (10, 17) and (22, 9)? (a) (13, 16) (b) (32, 26) (c) (6, 4) (d) (16, 13)
  39. 39.What is the midpoint of the line joining (1, 21) and (3, 9)? (a) (15, 2) (b) (1, 6) (c) (2, 15) (d) (4, 30)
  40. 40.What is the distance between the points (9, 11) and (17, 5)? (a) 14 (b) 10 (c) 11 (d) 100

Answer key

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

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