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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 201 · 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 (0, 6) and (8, 0)? (a) 100 (b) 11 (c) 10 (d) 14
  2. 2.What is the distance between the points (6, 7) and (18, 23)? (a) 20 (b) 400 (c) 28 (d) 21
  3. 3.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 17 (c) 14 (d) 13
  4. 4.What is the distance between the points (8, 13) and (32, 6)? (a) 26 (b) 625 (c) 25 (d) 31
  5. 5.In which quadrant does the point (5, −9) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  6. 6.What is the distance between the points (8, 16) and (14, 8)? (a) 100 (b) 10 (c) 14 (d) 11
  7. 7.What is the distance between the points (1, 4) and (5, 7)? (a) 25 (b) 6 (c) 7 (d) 5
  8. 8.What is the midpoint of the line joining (9, 6) and (19, 14)? (a) (10, 14) (b) (14, 10) (c) (5, 4) (d) (28, 20)
  9. 9.What is the distance between the points (0, 0) and (16, 12)? (a) 28 (b) 20 (c) 21 (d) 400
  10. 10.In which quadrant does the point (−2, 7) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  11. 11.What is the midpoint of the line joining (3, 10) and (5, 14)? (a) (1, 2) (b) (12, 4) (c) (8, 24) (d) (4, 12)
  12. 12.In which quadrant does the point (−3, 3) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  13. 13.What is the midpoint of the line joining (8, 19) and (16, 9)? (a) (12, 14) (b) (14, 12) (c) (24, 28) (d) (4, 5)
  14. 14.What is the distance between the points (7, 3) and (15, 9)? (a) 11 (b) 10 (c) 100 (d) 14
  15. 15.In which quadrant does the point (−9, 4) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  16. 16.What is the distance between the points (9, 6) and (15, 14)? (a) 14 (b) 11 (c) 100 (d) 10
  17. 17.What is the distance between the points (2, 7) and (14, 2)? (a) 14 (b) 169 (c) 13 (d) 17
  18. 18.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 20 (c) 400 (d) 21
  19. 19.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 11 (c) 14 (d) 100
  20. 20.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 28 (c) 21 (d) 400
  21. 21.What is the midpoint of the line joining (6, 20) and (16, 8)? (a) (14, 11) (b) (22, 28) (c) (11, 14) (d) (5, 6)
  22. 22.What is the midpoint of the line joining (5, 10) and (15, 6)? (a) (5, 2) (b) (8, 10) (c) (20, 16) (d) (10, 8)
  23. 23.What is the midpoint of the line joining (7, 0) and (9, 12)? (a) (16, 12) (b) (6, 8) (c) (1, 6) (d) (8, 6)
  24. 24.In which quadrant does the point (−5, −2) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  25. 25.What is the distance between the points (7, 8) and (14, 32)? (a) 625 (b) 31 (c) 26 (d) 25
  26. 26.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 7 (c) 5 (d) 6
  27. 27.How far is the point (9, 12) from the origin (0, 0)? (a) 15 (b) 225 (c) 16 (d) 21
  28. 28.In which quadrant does the point (6, 1) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  29. 29.In which quadrant does the point (−1, 2) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  30. 30.What is the distance between the points (0, 1) and (7, 25)? (a) 625 (b) 26 (c) 25 (d) 31
  31. 31.What is the distance between the points (9, 9) and (16, 33)? (a) 31 (b) 26 (c) 25 (d) 625
  32. 32.What is the midpoint of the line joining (10, 0) and (14, 6)? (a) (3, 12) (b) (24, 6) (c) (12, 3) (d) (2, 3)
  33. 33.In which quadrant does the point (−8, −7) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  34. 34.What is the distance between the points (4, 3) and (7, 7)? (a) 5 (b) 6 (c) 25 (d) 7
  35. 35.What is the distance between the points (7, 2) and (31, 9)? (a) 26 (b) 31 (c) 625 (d) 25
  36. 36.What is the midpoint of the line joining (4, 1) and (6, 11)? (a) (10, 12) (b) (6, 5) (c) (1, 5) (d) (5, 6)
  37. 37.What is the distance between the points (1, 2) and (9, 8)? (a) 11 (b) 14 (c) 100 (d) 10
  38. 38.In which quadrant does the point (5, −5) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  39. 39.What is the midpoint of the line joining (6, 1) and (18, 11)? (a) (6, 5) (b) (24, 12) (c) (12, 6) (d) (6, 12)
  40. 40.In which quadrant does the point (−3, 6) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant

Answer key

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

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