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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 474 · 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 (8, 3) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  2. 2.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 289 (c) 23 (d) 18
  3. 3.What is the distance between the points (6, 16) and (14, 1)? (a) 17 (b) 289 (c) 18 (d) 23
  4. 4.What is the distance between the points (0, 4) and (3, 0)? (a) 25 (b) 7 (c) 6 (d) 5
  5. 5.In which quadrant does the point (3, −4) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  6. 6.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 21 (c) 400 (d) 28
  7. 7.What is the midpoint of the line joining (0, 0) and (6, 4)? (a) (3, 2) (b) (6, 4) (c) (2, 3) (d) (4, 2)
  8. 8.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 100 (c) 11 (d) 10
  9. 9.In which quadrant does the point (−4, −4) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  10. 10.What is the midpoint of the line joining (7, 11) and (17, 1)? (a) (24, 12) (b) (5, 5) (c) (12, 6) (d) (6, 12)
  11. 11.What is the midpoint of the line joining (10, 3) and (16, 5)? (a) (3, 1) (b) (4, 13) (c) (13, 4) (d) (26, 8)
  12. 12.What is the midpoint of the line joining (5, 10) and (7, 2)? (a) (12, 12) (b) (1, 4) (c) (7, 6) (d) (6, 6)
  13. 13.What is the distance between the points (3, 15) and (19, 3)? (a) 21 (b) 28 (c) 20 (d) 400
  14. 14.What is the distance between the points (7, 7) and (19, 16)? (a) 225 (b) 16 (c) 15 (d) 21
  15. 15.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 625 (c) 25 (d) 31
  16. 16.What is the distance between the points (6, 0) and (10, 3)? (a) 5 (b) 7 (c) 6 (d) 25
  17. 17.What is the midpoint of the line joining (1, 12) and (9, 2)? (a) (4, 5) (b) (5, 7) (c) (10, 14) (d) (7, 5)
  18. 18.In which quadrant does the point (−2, 2) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  19. 19.What is the midpoint of the line joining (10, 2) and (20, 12)? (a) (7, 15) (b) (5, 5) (c) (30, 14) (d) (15, 7)
  20. 20.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 15 (c) 225 (d) 16
  21. 21.What is the distance between the points (2, 11) and (17, 3)? (a) 18 (b) 23 (c) 17 (d) 289
  22. 22.What is the distance between the points (3, 15) and (9, 7)? (a) 14 (b) 11 (c) 10 (d) 100
  23. 23.In which quadrant does the point (3, 9) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  24. 24.What is the midpoint of the line joining (0, 0) and (2, 8)? (a) (2, 8) (b) (1, 4) (c) (2, 4) (d) (4, 1)
  25. 25.In which quadrant does the point (1, 3) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  26. 26.In which quadrant does the point (−5, 7) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  27. 27.What is the distance between the points (7, 6) and (10, 2)? (a) 25 (b) 7 (c) 6 (d) 5
  28. 28.What is the midpoint of the line joining (10, 17) and (16, 9)? (a) (26, 26) (b) (13, 13) (c) (14, 13) (d) (3, 4)
  29. 29.In which quadrant does the point (1, −3) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  30. 30.In which quadrant does the point (−8, 2) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  31. 31.What is the distance between the points (9, 1) and (18, 13)? (a) 15 (b) 225 (c) 21 (d) 16
  32. 32.What is the midpoint of the line joining (9, 4) and (15, 6)? (a) (5, 12) (b) (24, 10) (c) (12, 5) (d) (3, 1)
  33. 33.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 169 (c) 17 (d) 13
  34. 34.What is the midpoint of the line joining (0, 8) and (6, 4)? (a) (6, 3) (b) (6, 12) (c) (3, 6) (d) (3, 2)
  35. 35.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 26 (c) 25 (d) 625
  36. 36.In which quadrant does the point (7, 1) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  37. 37.What is the midpoint of the line joining (4, 5) and (6, 1)? (a) (1, 2) (b) (5, 3) (c) (10, 6) (d) (3, 5)
  38. 38.What is the distance between the points (7, 3) and (23, 15)? (a) 400 (b) 21 (c) 20 (d) 28
  39. 39.In which quadrant does the point (−7, 6) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  40. 40.What is the distance between the points (0, 6) and (7, 30)? (a) 25 (b) 625 (c) 26 (d) 31

Answer key

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

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