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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 167 · 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 (4, −2) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  2. 2.What is the distance between the points (1, 1) and (9, 16)? (a) 18 (b) 23 (c) 289 (d) 17
  3. 3.In which quadrant does the point (−8, −9) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  4. 4.What is the distance between the points (6, 5) and (30, 12)? (a) 26 (b) 31 (c) 625 (d) 25
  5. 5.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 6 (c) 25 (d) 5
  6. 6.In which quadrant does the point (8, −2) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  7. 7.What is the distance between the points (8, 12) and (32, 5)? (a) 26 (b) 625 (c) 25 (d) 31
  8. 8.In which quadrant does the point (−1, −9) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  9. 9.What is the distance between the points (8, 2) and (20, 11)? (a) 225 (b) 21 (c) 15 (d) 16
  10. 10.What is the midpoint of the line joining (7, 20) and (13, 8)? (a) (14, 10) (b) (20, 28) (c) (10, 14) (d) (3, 6)
  11. 11.In which quadrant does the point (1, −1) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  12. 12.What is the distance between the points (3, 2) and (15, 18)? (a) 28 (b) 400 (c) 20 (d) 21
  13. 13.In which quadrant does the point (9, −3) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  14. 14.What is the midpoint of the line joining (1, 9) and (13, 21)? (a) (6, 6) (b) (14, 30) (c) (7, 15) (d) (15, 7)
  15. 15.In which quadrant does the point (5, 8) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  16. 16.What is the distance between the points (6, 26) and (13, 2)? (a) 625 (b) 25 (c) 31 (d) 26
  17. 17.What is the distance between the points (3, 17) and (11, 2)? (a) 289 (b) 23 (c) 17 (d) 18
  18. 18.What is the midpoint of the line joining (9, 16) and (21, 10)? (a) (30, 26) (b) (15, 13) (c) (13, 15) (d) (6, 3)
  19. 19.In which quadrant does the point (4, 7) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  20. 20.In which quadrant does the point (3, 2) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  21. 21.What is the midpoint of the line joining (3, 8) and (11, 12)? (a) (14, 20) (b) (4, 2) (c) (7, 10) (d) (10, 7)
  22. 22.What is the distance between the points (6, 3) and (15, 15)? (a) 225 (b) 21 (c) 16 (d) 15
  23. 23.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 21 (c) 400 (d) 20
  24. 24.What is the distance between the points (6, 14) and (30, 7)? (a) 26 (b) 31 (c) 625 (d) 25
  25. 25.What is the midpoint of the line joining (8, 11) and (20, 1)? (a) (6, 5) (b) (28, 12) (c) (14, 6) (d) (6, 14)
  26. 26.What is the distance between the points (6, 10) and (18, 1)? (a) 21 (b) 16 (c) 225 (d) 15
  27. 27.What is the midpoint of the line joining (4, 0) and (16, 6)? (a) (3, 10) (b) (6, 3) (c) (20, 6) (d) (10, 3)
  28. 28.What is the distance between the points (7, 1) and (13, 9)? (a) 14 (b) 100 (c) 11 (d) 10
  29. 29.In which quadrant does the point (−4, 6) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  30. 30.What is the midpoint of the line joining (1, 3) and (7, 1)? (a) (4, 2) (b) (8, 4) (c) (2, 4) (d) (3, 1)
  31. 31.What is the distance between the points (7, 6) and (16, 18)? (a) 21 (b) 15 (c) 16 (d) 225
  32. 32.What is the distance between the points (1, 8) and (13, 24)? (a) 21 (b) 400 (c) 20 (d) 28
  33. 33.What is the distance between the points (8, 8) and (13, 20)? (a) 17 (b) 13 (c) 14 (d) 169
  34. 34.In which quadrant does the point (−8, −2) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  35. 35.What is the distance between the points (1, 3) and (7, 11)? (a) 10 (b) 14 (c) 11 (d) 100
  36. 36.What is the distance between the points (1, 6) and (25, 13)? (a) 625 (b) 31 (c) 25 (d) 26
  37. 37.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 18 (c) 23 (d) 17
  38. 38.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 28 (c) 400 (d) 21
  39. 39.What is the midpoint of the line joining (1, 11) and (13, 3)? (a) (7, 7) (b) (14, 14) (c) (6, 4) (d) (8, 7)
  40. 40.In which quadrant does the point (3, 9) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant

Answer key

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

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