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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 248 · 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, 7) and (3, 11)? (a) 7 (b) 5 (c) 25 (d) 6
  2. 2.What is the distance between the points (8, 8) and (14, 16)? (a) 10 (b) 100 (c) 14 (d) 11
  3. 3.What is the midpoint of the line joining (4, 10) and (14, 2)? (a) (5, 4) (b) (9, 6) (c) (6, 9) (d) (18, 12)
  4. 4.What is the distance between the points (3, 8) and (15, 17)? (a) 16 (b) 15 (c) 225 (d) 21
  5. 5.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 11 (c) 14 (d) 10
  6. 6.What is the midpoint of the line joining (7, 5) and (9, 1)? (a) (16, 6) (b) (1, 2) (c) (8, 3) (d) (3, 8)
  7. 7.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 20 (c) 21 (d) 28
  8. 8.What is the distance between the points (6, 7) and (9, 3)? (a) 6 (b) 5 (c) 7 (d) 25
  9. 9.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 625 (c) 25 (d) 31
  10. 10.What is the distance between the points (9, 27) and (16, 3)? (a) 625 (b) 26 (c) 31 (d) 25
  11. 11.What is the distance between the points (5, 5) and (9, 2)? (a) 7 (b) 5 (c) 6 (d) 25
  12. 12.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 28 (c) 400 (d) 21
  13. 13.In which quadrant does the point (−2, 8) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  14. 14.In which quadrant does the point (−8, −2) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  15. 15.What is the midpoint of the line joining (1, 9) and (7, 5)? (a) (8, 14) (b) (3, 2) (c) (7, 4) (d) (4, 7)
  16. 16.What is the midpoint of the line joining (8, 4) and (20, 6)? (a) (6, 1) (b) (28, 10) (c) (14, 5) (d) (5, 14)
  17. 17.In which quadrant does the point (−3, 9) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  18. 18.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 17 (c) 18 (d) 289
  19. 19.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 5 (c) 7 (d) 6
  20. 20.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 100 (c) 14 (d) 10
  21. 21.In which quadrant does the point (3, 8) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  22. 22.In which quadrant does the point (−3, 2) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  23. 23.What is the distance between the points (1, 19) and (10, 7)? (a) 21 (b) 16 (c) 15 (d) 225
  24. 24.What is the distance between the points (6, 11) and (10, 8)? (a) 5 (b) 7 (c) 6 (d) 25
  25. 25.What is the distance between the points (6, 2) and (13, 26)? (a) 31 (b) 25 (c) 625 (d) 26
  26. 26.In which quadrant does the point (−6, 4) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  27. 27.What is the distance between the points (7, 8) and (13, 16)? (a) 100 (b) 11 (c) 14 (d) 10
  28. 28.What is the distance between the points (1, 8) and (25, 15)? (a) 25 (b) 625 (c) 26 (d) 31
  29. 29.What is the midpoint of the line joining (2, 0) and (4, 6)? (a) (1, 3) (b) (6, 6) (c) (4, 3) (d) (3, 3)
  30. 30.In which quadrant does the point (3, −6) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  31. 31.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 25 (c) 7 (d) 5
  32. 32.What is the distance between the points (7, 7) and (10, 11)? (a) 25 (b) 7 (c) 6 (d) 5
  33. 33.In which quadrant does the point (−2, 3) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  34. 34.What is the midpoint of the line joining (8, 10) and (16, 20)? (a) (4, 5) (b) (12, 15) (c) (24, 30) (d) (15, 12)
  35. 35.In which quadrant does the point (−8, −7) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  36. 36.What is the distance between the points (8, 5) and (20, 21)? (a) 21 (b) 20 (c) 400 (d) 28
  37. 37.What is the distance between the points (6, 1) and (30, 8)? (a) 625 (b) 26 (c) 25 (d) 31
  38. 38.In which quadrant does the point (−9, 5) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  39. 39.What is the distance between the points (4, 17) and (12, 2)? (a) 17 (b) 18 (c) 23 (d) 289
  40. 40.What is the midpoint of the line joining (1, 10) and (5, 18)? (a) (6, 28) (b) (14, 3) (c) (2, 4) (d) (3, 14)

Answer key

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

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