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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 354 · 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 (8, 15) from the origin (0, 0)? (a) 289 (b) 23 (c) 18 (d) 17
  2. 2.What is the distance between the points (2, 9) and (6, 12)? (a) 6 (b) 7 (c) 5 (d) 25
  3. 3.What is the midpoint of the line joining (0, 10) and (12, 2)? (a) (6, 4) (b) (7, 6) (c) (6, 6) (d) (12, 12)
  4. 4.In which quadrant does the point (−7, 2) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  5. 5.What is the distance between the points (4, 2) and (16, 7)? (a) 14 (b) 169 (c) 13 (d) 17
  6. 6.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 11 (c) 100 (d) 14
  7. 7.In which quadrant does the point (2, 2) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  8. 8.In which quadrant does the point (4, −4) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  9. 9.What is the distance between the points (2, 2) and (14, 18)? (a) 28 (b) 400 (c) 21 (d) 20
  10. 10.In which quadrant does the point (−1, −7) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  11. 11.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 169 (c) 17 (d) 13
  12. 12.What is the distance between the points (0, 2) and (7, 26)? (a) 26 (b) 25 (c) 625 (d) 31
  13. 13.What is the midpoint of the line joining (1, 0) and (9, 4)? (a) (2, 5) (b) (10, 4) (c) (4, 2) (d) (5, 2)
  14. 14.What is the distance between the points (9, 5) and (21, 21)? (a) 28 (b) 21 (c) 20 (d) 400
  15. 15.In which quadrant does the point (−3, −5) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  16. 16.What is the distance between the points (4, 0) and (9, 12)? (a) 17 (b) 14 (c) 13 (d) 169
  17. 17.What is the distance between the points (9, 8) and (33, 1)? (a) 25 (b) 625 (c) 26 (d) 31
  18. 18.What is the midpoint of the line joining (4, 5) and (8, 7)? (a) (7, 6) (b) (12, 12) (c) (6, 6) (d) (2, 1)
  19. 19.What is the distance between the points (5, 12) and (10, 0)? (a) 14 (b) 17 (c) 13 (d) 169
  20. 20.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 26 (c) 25 (d) 625
  21. 21.What is the midpoint of the line joining (5, 9) and (15, 19)? (a) (10, 14) (b) (5, 5) (c) (14, 10) (d) (20, 28)
  22. 22.What is the midpoint of the line joining (7, 8) and (15, 18)? (a) (13, 11) (b) (4, 5) (c) (11, 13) (d) (22, 26)
  23. 23.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 23 (c) 17 (d) 289
  24. 24.In which quadrant does the point (−8, −9) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  25. 25.What is the distance between the points (4, 1) and (11, 25)? (a) 625 (b) 25 (c) 26 (d) 31
  26. 26.In which quadrant does the point (2, 1) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  27. 27.In which quadrant does the point (5, 9) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  28. 28.What is the distance between the points (4, 6) and (16, 11)? (a) 17 (b) 14 (c) 13 (d) 169
  29. 29.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 7 (c) 6 (d) 5
  30. 30.What is the distance between the points (8, 9) and (12, 12)? (a) 6 (b) 5 (c) 25 (d) 7
  31. 31.What is the distance between the points (1, 13) and (4, 9)? (a) 6 (b) 7 (c) 5 (d) 25
  32. 32.What is the distance between the points (9, 4) and (18, 16)? (a) 21 (b) 16 (c) 225 (d) 15
  33. 33.What is the distance between the points (9, 16) and (25, 4)? (a) 400 (b) 28 (c) 21 (d) 20
  34. 34.In which quadrant does the point (2, −4) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  35. 35.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 28 (c) 400 (d) 20
  36. 36.What is the midpoint of the line joining (9, 11) and (13, 3)? (a) (2, 4) (b) (11, 7) (c) (22, 14) (d) (7, 11)
  37. 37.What is the midpoint of the line joining (4, 14) and (16, 6)? (a) (10, 10) (b) (6, 4) (c) (11, 10) (d) (20, 20)
  38. 38.In which quadrant does the point (−5, 1) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  39. 39.In which quadrant does the point (5, 3) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  40. 40.In which quadrant does the point (−4, 7) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant

Answer key

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

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