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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 41 · 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 (2, −1) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  2. 2.In which quadrant does the point (3, 2) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  3. 3.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 15 (c) 16 (d) 225
  4. 4.In which quadrant does the point (−4, 2) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  5. 5.What is the midpoint of the line joining (1, 17) and (3, 5)? (a) (11, 2) (b) (2, 11) (c) (4, 22) (d) (1, 6)
  6. 6.What is the distance between the points (4, 0) and (16, 9)? (a) 16 (b) 225 (c) 15 (d) 21
  7. 7.What is the midpoint of the line joining (9, 7) and (21, 15)? (a) (30, 22) (b) (15, 11) (c) (11, 15) (d) (6, 4)
  8. 8.What is the midpoint of the line joining (0, 5) and (4, 3)? (a) (2, 1) (b) (4, 2) (c) (2, 4) (d) (4, 8)
  9. 9.In which quadrant does the point (9, 9) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  10. 10.How far is the point (12, 16) from the origin (0, 0)? (a) 20 (b) 21 (c) 28 (d) 400
  11. 11.What is the midpoint of the line joining (1, 6) and (9, 18)? (a) (4, 6) (b) (12, 5) (c) (10, 24) (d) (5, 12)
  12. 12.What is the distance between the points (7, 8) and (19, 3)? (a) 13 (b) 14 (c) 17 (d) 169
  13. 13.In which quadrant does the point (7, 5) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  14. 14.In which quadrant does the point (−1, −2) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  15. 15.What is the midpoint of the line joining (9, 13) and (13, 7)? (a) (11, 10) (b) (2, 3) (c) (22, 20) (d) (10, 11)
  16. 16.In which quadrant does the point (1, 3) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  17. 17.What is the distance between the points (0, 20) and (16, 8)? (a) 28 (b) 400 (c) 21 (d) 20
  18. 18.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 25 (c) 5 (d) 7
  19. 19.What is the distance between the points (8, 17) and (24, 5)? (a) 400 (b) 20 (c) 28 (d) 21
  20. 20.What is the distance between the points (6, 8) and (10, 11)? (a) 7 (b) 25 (c) 6 (d) 5
  21. 21.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 13 (c) 169 (d) 17
  22. 22.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 625 (c) 26 (d) 25
  23. 23.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 20 (c) 21 (d) 400
  24. 24.In which quadrant does the point (6, 5) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  25. 25.What is the distance between the points (8, 8) and (11, 4)? (a) 7 (b) 5 (c) 25 (d) 6
  26. 26.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 23 (c) 18 (d) 17
  27. 27.What is the distance between the points (2, 0) and (6, 3)? (a) 7 (b) 5 (c) 25 (d) 6
  28. 28.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 25 (c) 5 (d) 7
  29. 29.In which quadrant does the point (6, −5) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  30. 30.What is the distance between the points (1, 8) and (5, 5)? (a) 7 (b) 5 (c) 6 (d) 25
  31. 31.What is the distance between the points (4, 5) and (12, 11)? (a) 14 (b) 11 (c) 100 (d) 10
  32. 32.What is the distance between the points (0, 0) and (7, 24)? (a) 31 (b) 625 (c) 25 (d) 26
  33. 33.What is the distance between the points (2, 4) and (6, 7)? (a) 7 (b) 5 (c) 6 (d) 25
  34. 34.What is the midpoint of the line joining (5, 8) and (11, 4)? (a) (8, 6) (b) (3, 2) (c) (6, 8) (d) (16, 12)
  35. 35.In which quadrant does the point (−4, 1) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  36. 36.What is the distance between the points (0, 7) and (4, 10)? (a) 6 (b) 25 (c) 7 (d) 5
  37. 37.What is the distance between the points (9, 1) and (21, 17)? (a) 21 (b) 20 (c) 28 (d) 400
  38. 38.What is the distance between the points (1, 20) and (17, 8)? (a) 21 (b) 28 (c) 20 (d) 400
  39. 39.What is the midpoint of the line joining (5, 18) and (9, 8)? (a) (2, 5) (b) (13, 7) (c) (7, 13) (d) (14, 26)
  40. 40.What is the midpoint of the line joining (1, 11) and (5, 9)? (a) (2, 1) (b) (6, 20) (c) (3, 10) (d) (10, 3)

Answer key

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

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