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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 108 · 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 midpoint of the line joining (9, 10) and (21, 16)? (a) (30, 26) (b) (15, 13) (c) (13, 15) (d) (6, 3)
  2. 2.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 100 (c) 14 (d) 10
  3. 3.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 26 (c) 31 (d) 25
  4. 4.What is the distance between the points (3, 7) and (10, 31)? (a) 26 (b) 25 (c) 625 (d) 31
  5. 5.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 14 (c) 11 (d) 10
  6. 6.What is the midpoint of the line joining (2, 7) and (8, 3)? (a) (3, 2) (b) (10, 10) (c) (5, 5) (d) (6, 5)
  7. 7.What is the distance between the points (2, 14) and (26, 7)? (a) 625 (b) 25 (c) 26 (d) 31
  8. 8.In which quadrant does the point (7, −6) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  9. 9.In which quadrant does the point (−2, −8) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  10. 10.In which quadrant does the point (7, 8) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  11. 11.What is the distance between the points (3, 5) and (15, 10)? (a) 169 (b) 14 (c) 17 (d) 13
  12. 12.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 17 (c) 18 (d) 23
  13. 13.In which quadrant does the point (−5, −1) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  14. 14.In which quadrant does the point (7, −3) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  15. 15.What is the distance between the points (9, 8) and (25, 20)? (a) 20 (b) 28 (c) 21 (d) 400
  16. 16.What is the midpoint of the line joining (7, 0) and (17, 12)? (a) (5, 6) (b) (6, 12) (c) (24, 12) (d) (12, 6)
  17. 17.In which quadrant does the point (1, 9) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  18. 18.In which quadrant does the point (8, −9) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  19. 19.In which quadrant does the point (−1, 8) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  20. 20.What is the midpoint of the line joining (6, 15) and (18, 5)? (a) (24, 20) (b) (10, 12) (c) (6, 5) (d) (12, 10)
  21. 21.How far is the point (12, 9) from the origin (0, 0)? (a) 15 (b) 16 (c) 21 (d) 225
  22. 22.What is the midpoint of the line joining (9, 22) and (17, 10)? (a) (13, 16) (b) (4, 6) (c) (26, 32) (d) (16, 13)
  23. 23.What is the midpoint of the line joining (8, 10) and (12, 0)? (a) (20, 10) (b) (2, 5) (c) (10, 5) (d) (5, 10)
  24. 24.How far is the point (9, 12) from the origin (0, 0)? (a) 15 (b) 21 (c) 225 (d) 16
  25. 25.In which quadrant does the point (1, 5) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  26. 26.What is the distance between the points (4, 0) and (10, 8)? (a) 14 (b) 11 (c) 100 (d) 10
  27. 27.What is the distance between the points (9, 0) and (13, 3)? (a) 25 (b) 7 (c) 5 (d) 6
  28. 28.In which quadrant does the point (−3, −5) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  29. 29.What is the midpoint of the line joining (2, 15) and (6, 3)? (a) (4, 9) (b) (9, 4) (c) (8, 18) (d) (2, 6)
  30. 30.In which quadrant does the point (1, 2) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  31. 31.What is the distance between the points (4, 7) and (16, 16)? (a) 15 (b) 21 (c) 16 (d) 225
  32. 32.In which quadrant does the point (−5, −5) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  33. 33.What is the distance between the points (2, 6) and (14, 22)? (a) 28 (b) 20 (c) 400 (d) 21
  34. 34.How far is the point (5, 12) from the origin (0, 0)? (a) 13 (b) 17 (c) 14 (d) 169
  35. 35.What is the distance between the points (7, 19) and (23, 7)? (a) 21 (b) 400 (c) 20 (d) 28
  36. 36.What is the distance between the points (6, 20) and (11, 8)? (a) 169 (b) 13 (c) 14 (d) 17
  37. 37.What is the distance between the points (0, 7) and (15, 15)? (a) 23 (b) 289 (c) 18 (d) 17
  38. 38.What is the midpoint of the line joining (6, 10) and (10, 6)? (a) (2, 2) (b) (9, 8) (c) (8, 8) (d) (16, 16)
  39. 39.What is the distance between the points (4, 6) and (8, 3)? (a) 5 (b) 25 (c) 7 (d) 6
  40. 40.In which quadrant does the point (4, −2) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant

Answer key

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

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