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Coordinate Geometry Worksheet for Maths Olympiad

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

Answer key

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

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