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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 703 · 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.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 10 (c) 100 (d) 11
  2. 2.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 13 (c) 14 (d) 17
  3. 3.In which quadrant does the point (−7, 8) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  4. 4.In which quadrant does the point (−1, 6) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  5. 5.In which quadrant does the point (1, 9) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  6. 6.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 400 (c) 28 (d) 20
  7. 7.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 28 (c) 400 (d) 21
  8. 8.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 26 (c) 31 (d) 25
  9. 9.In which quadrant does the point (−5, −3) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  10. 10.What is the distance between the points (0, 12) and (12, 7)? (a) 14 (b) 169 (c) 17 (d) 13
  11. 11.How far is the point (7, 24) from the origin (0, 0)? (a) 25 (b) 625 (c) 26 (d) 31
  12. 12.What is the distance between the points (8, 6) and (14, 14)? (a) 100 (b) 14 (c) 10 (d) 11
  13. 13.In which quadrant does the point (1, −7) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  14. 14.What is the distance between the points (8, 17) and (24, 5)? (a) 20 (b) 28 (c) 21 (d) 400
  15. 15.What is the distance between the points (3, 12) and (15, 3)? (a) 21 (b) 16 (c) 225 (d) 15
  16. 16.What is the midpoint of the line joining (2, 16) and (6, 6)? (a) (8, 22) (b) (4, 11) (c) (2, 5) (d) (11, 4)
  17. 17.What is the midpoint of the line joining (1, 12) and (3, 10)? (a) (1, 1) (b) (11, 2) (c) (4, 22) (d) (2, 11)
  18. 18.What is the distance between the points (8, 1) and (16, 16)? (a) 17 (b) 23 (c) 289 (d) 18
  19. 19.What is the distance between the points (3, 3) and (7, 0)? (a) 7 (b) 5 (c) 25 (d) 6
  20. 20.In which quadrant does the point (−2, 3) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  21. 21.What is the midpoint of the line joining (1, 9) and (9, 7)? (a) (5, 8) (b) (8, 5) (c) (10, 16) (d) (4, 1)
  22. 22.What is the midpoint of the line joining (0, 1) and (4, 3)? (a) (3, 2) (b) (4, 4) (c) (2, 2) (d) (2, 1)
  23. 23.What is the midpoint of the line joining (0, 2) and (2, 8)? (a) (2, 10) (b) (5, 1) (c) (1, 5) (d) (1, 3)
  24. 24.What is the midpoint of the line joining (3, 18) and (5, 8)? (a) (8, 26) (b) (13, 4) (c) (1, 5) (d) (4, 13)
  25. 25.In which quadrant does the point (9, 7) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  26. 26.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 6 (c) 7 (d) 5
  27. 27.What is the distance between the points (6, 12) and (10, 9)? (a) 7 (b) 6 (c) 5 (d) 25
  28. 28.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 6 (c) 5 (d) 25
  29. 29.What is the midpoint of the line joining (1, 8) and (11, 2)? (a) (12, 10) (b) (5, 6) (c) (6, 5) (d) (5, 3)
  30. 30.What is the midpoint of the line joining (2, 0) and (14, 4)? (a) (2, 8) (b) (6, 2) (c) (16, 4) (d) (8, 2)
  31. 31.In which quadrant does the point (3, 1) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  32. 32.What is the distance between the points (7, 1) and (23, 13)? (a) 400 (b) 28 (c) 21 (d) 20
  33. 33.What is the midpoint of the line joining (9, 5) and (15, 7)? (a) (24, 12) (b) (3, 1) (c) (12, 6) (d) (6, 12)
  34. 34.What is the midpoint of the line joining (3, 10) and (9, 4)? (a) (6, 7) (b) (12, 14) (c) (7, 6) (d) (3, 3)
  35. 35.In which quadrant does the point (1, 4) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  36. 36.In which quadrant does the point (1, −5) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  37. 37.In which quadrant does the point (−1, −2) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  38. 38.What is the midpoint of the line joining (0, 16) and (12, 4)? (a) (6, 6) (b) (6, 10) (c) (12, 20) (d) (10, 6)
  39. 39.In which quadrant does the point (8, 9) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  40. 40.What is the distance between the points (4, 2) and (20, 14)? (a) 400 (b) 28 (c) 21 (d) 20

Answer key

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

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