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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 180 · 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 distance between the points (0, 13) and (12, 4)? (a) 15 (b) 16 (c) 225 (d) 21
  2. 2.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 400 (c) 20 (d) 21
  3. 3.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 400 (c) 28 (d) 20
  4. 4.In which quadrant does the point (7, −6) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  5. 5.In which quadrant does the point (5, −1) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  6. 6.In which quadrant does the point (−2, 7) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  7. 7.In which quadrant does the point (−5, 2) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  8. 8.What is the midpoint of the line joining (10, 10) and (14, 14)? (a) (12, 12) (b) (24, 24) (c) (2, 2) (d) (13, 12)
  9. 9.What is the midpoint of the line joining (4, 20) and (16, 10)? (a) (15, 10) (b) (6, 5) (c) (20, 30) (d) (10, 15)
  10. 10.What is the distance between the points (6, 1) and (11, 13)? (a) 17 (b) 169 (c) 14 (d) 13
  11. 11.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 17 (c) 13 (d) 169
  12. 12.What is the midpoint of the line joining (9, 2) and (11, 14)? (a) (8, 10) (b) (20, 16) (c) (10, 8) (d) (1, 6)
  13. 13.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 13 (c) 169 (d) 14
  14. 14.In which quadrant does the point (−9, −8) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  15. 15.What is the distance between the points (0, 5) and (6, 13)? (a) 10 (b) 14 (c) 100 (d) 11
  16. 16.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 25 (c) 26 (d) 31
  17. 17.What is the distance between the points (8, 9) and (16, 15)? (a) 10 (b) 11 (c) 100 (d) 14
  18. 18.What is the distance between the points (3, 15) and (11, 0)? (a) 18 (b) 17 (c) 289 (d) 23
  19. 19.What is the midpoint of the line joining (1, 2) and (7, 0)? (a) (3, 1) (b) (1, 4) (c) (4, 1) (d) (8, 2)
  20. 20.What is the distance between the points (4, 6) and (8, 3)? (a) 25 (b) 7 (c) 5 (d) 6
  21. 21.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 225 (c) 15 (d) 21
  22. 22.In which quadrant does the point (6, 3) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  23. 23.What is the distance between the points (0, 1) and (5, 13)? (a) 169 (b) 17 (c) 14 (d) 13
  24. 24.What is the distance between the points (1, 8) and (17, 20)? (a) 28 (b) 400 (c) 21 (d) 20
  25. 25.In which quadrant does the point (4, 6) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  26. 26.What is the distance between the points (6, 7) and (18, 16)? (a) 21 (b) 16 (c) 225 (d) 15
  27. 27.What is the distance between the points (7, 8) and (19, 3)? (a) 17 (b) 169 (c) 13 (d) 14
  28. 28.In which quadrant does the point (−8, 6) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  29. 29.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 7 (c) 5 (d) 25
  30. 30.What is the distance between the points (3, 16) and (8, 4)? (a) 13 (b) 17 (c) 14 (d) 169
  31. 31.What is the midpoint of the line joining (7, 8) and (13, 14)? (a) (20, 22) (b) (10, 11) (c) (3, 3) (d) (11, 10)
  32. 32.What is the midpoint of the line joining (0, 3) and (6, 1)? (a) (6, 4) (b) (3, 2) (c) (2, 3) (d) (3, 1)
  33. 33.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 289 (c) 17 (d) 23
  34. 34.What is the distance between the points (7, 19) and (16, 7)? (a) 225 (b) 15 (c) 16 (d) 21
  35. 35.In which quadrant does the point (2, 4) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  36. 36.In which quadrant does the point (7, −1) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  37. 37.In which quadrant does the point (8, 6) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  38. 38.What is the midpoint of the line joining (2, 17) and (6, 9)? (a) (13, 4) (b) (2, 4) (c) (8, 26) (d) (4, 13)
  39. 39.In which quadrant does the point (1, 7) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  40. 40.What is the distance between the points (2, 27) and (9, 3)? (a) 26 (b) 25 (c) 31 (d) 625

Answer key

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

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