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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 48 · 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) 17 (b) 289 (c) 18 (d) 23
  2. 2.In which quadrant does the point (7, 4) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  3. 3.What is the midpoint of the line joining (0, 10) and (2, 16)? (a) (13, 1) (b) (2, 26) (c) (1, 13) (d) (1, 3)
  4. 4.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 100 (c) 14 (d) 10
  5. 5.What is the midpoint of the line joining (0, 8) and (4, 6)? (a) (4, 14) (b) (7, 2) (c) (2, 7) (d) (2, 1)
  6. 6.What is the midpoint of the line joining (2, 17) and (4, 7)? (a) (3, 12) (b) (6, 24) (c) (12, 3) (d) (1, 5)
  7. 7.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 14 (c) 13 (d) 169
  8. 8.In which quadrant does the point (8, −9) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  9. 9.In which quadrant does the point (−1, −9) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  10. 10.What is the midpoint of the line joining (2, 9) and (12, 1)? (a) (5, 4) (b) (5, 7) (c) (14, 10) (d) (7, 5)
  11. 11.In which quadrant does the point (8, 4) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  12. 12.What is the distance between the points (8, 0) and (20, 5)? (a) 169 (b) 17 (c) 14 (d) 13
  13. 13.In which quadrant does the point (−8, −9) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  14. 14.What is the distance between the points (8, 6) and (16, 0)? (a) 10 (b) 11 (c) 14 (d) 100
  15. 15.In which quadrant does the point (6, 5) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  16. 16.What is the midpoint of the line joining (5, 8) and (13, 10)? (a) (10, 9) (b) (18, 18) (c) (9, 9) (d) (4, 1)
  17. 17.What is the distance between the points (2, 7) and (9, 31)? (a) 26 (b) 31 (c) 625 (d) 25
  18. 18.What is the midpoint of the line joining (9, 9) and (21, 13)? (a) (11, 15) (b) (30, 22) (c) (15, 11) (d) (6, 2)
  19. 19.What is the distance between the points (5, 7) and (13, 22)? (a) 18 (b) 23 (c) 17 (d) 289
  20. 20.How far is the point (12, 16) from the origin (0, 0)? (a) 20 (b) 28 (c) 400 (d) 21
  21. 21.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 25 (c) 6 (d) 5
  22. 22.What is the distance between the points (5, 6) and (17, 22)? (a) 21 (b) 28 (c) 400 (d) 20
  23. 23.In which quadrant does the point (2, 4) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  24. 24.What is the distance between the points (1, 7) and (6, 19)? (a) 14 (b) 13 (c) 17 (d) 169
  25. 25.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 400 (c) 20 (d) 21
  26. 26.In which quadrant does the point (−2, 4) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  27. 27.What is the distance between the points (0, 9) and (4, 6)? (a) 5 (b) 25 (c) 7 (d) 6
  28. 28.In which quadrant does the point (6, −4) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  29. 29.In which quadrant does the point (−7, 4) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  30. 30.What is the distance between the points (2, 2) and (11, 14)? (a) 15 (b) 21 (c) 225 (d) 16
  31. 31.In which quadrant does the point (6, −7) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  32. 32.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 23 (c) 17 (d) 289
  33. 33.In which quadrant does the point (−7, −2) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  34. 34.What is the distance between the points (8, 9) and (20, 4)? (a) 17 (b) 13 (c) 14 (d) 169
  35. 35.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 16 (c) 15 (d) 225
  36. 36.What is the distance between the points (0, 17) and (12, 1)? (a) 400 (b) 21 (c) 28 (d) 20
  37. 37.What is the midpoint of the line joining (6, 19) and (12, 7)? (a) (9, 13) (b) (13, 9) (c) (3, 6) (d) (18, 26)
  38. 38.In which quadrant does the point (−8, 6) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  39. 39.What is the distance between the points (8, 2) and (15, 26)? (a) 26 (b) 25 (c) 625 (d) 31
  40. 40.What is the midpoint of the line joining (0, 11) and (2, 5)? (a) (1, 3) (b) (1, 8) (c) (2, 16) (d) (8, 1)

Answer key

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

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