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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 454 · 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 (4, 12) and (10, 4)? (a) 14 (b) 100 (c) 11 (d) 10
  2. 2.In which quadrant does the point (−1, 4) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  3. 3.What is the distance between the points (8, 2) and (15, 26)? (a) 625 (b) 31 (c) 26 (d) 25
  4. 4.What is the distance between the points (6, 2) and (18, 11)? (a) 225 (b) 16 (c) 15 (d) 21
  5. 5.What is the distance between the points (4, 1) and (20, 13)? (a) 400 (b) 20 (c) 21 (d) 28
  6. 6.What is the midpoint of the line joining (3, 0) and (7, 8)? (a) (2, 4) (b) (5, 4) (c) (4, 5) (d) (10, 8)
  7. 7.What is the midpoint of the line joining (0, 3) and (2, 5)? (a) (4, 1) (b) (1, 4) (c) (2, 8) (d) (1, 1)
  8. 8.How far is the point (16, 12) from the origin (0, 0)? (a) 400 (b) 28 (c) 21 (d) 20
  9. 9.In which quadrant does the point (−1, 5) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  10. 10.What is the midpoint of the line joining (1, 2) and (9, 12)? (a) (7, 5) (b) (5, 7) (c) (4, 5) (d) (10, 14)
  11. 11.In which quadrant does the point (−2, 9) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  12. 12.What is the distance between the points (7, 17) and (15, 2)? (a) 18 (b) 17 (c) 289 (d) 23
  13. 13.In which quadrant does the point (−2, 8) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  14. 14.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 6 (c) 5 (d) 7
  15. 15.What is the distance between the points (7, 12) and (23, 0)? (a) 21 (b) 20 (c) 400 (d) 28
  16. 16.What is the distance between the points (5, 6) and (9, 3)? (a) 7 (b) 5 (c) 25 (d) 6
  17. 17.What is the midpoint of the line joining (0, 1) and (10, 9)? (a) (10, 10) (b) (6, 5) (c) (5, 5) (d) (5, 4)
  18. 18.What is the midpoint of the line joining (9, 5) and (11, 13)? (a) (9, 10) (b) (10, 9) (c) (20, 18) (d) (1, 4)
  19. 19.What is the distance between the points (1, 3) and (13, 19)? (a) 28 (b) 21 (c) 20 (d) 400
  20. 20.In which quadrant does the point (4, 3) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  21. 21.What is the distance between the points (3, 12) and (6, 8)? (a) 25 (b) 7 (c) 6 (d) 5
  22. 22.What is the midpoint of the line joining (3, 20) and (9, 8)? (a) (12, 28) (b) (3, 6) (c) (14, 6) (d) (6, 14)
  23. 23.In which quadrant does the point (−9, 9) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  24. 24.What is the midpoint of the line joining (3, 0) and (7, 6)? (a) (2, 3) (b) (3, 5) (c) (10, 6) (d) (5, 3)
  25. 25.What is the midpoint of the line joining (0, 22) and (10, 10)? (a) (5, 6) (b) (5, 16) (c) (16, 5) (d) (10, 32)
  26. 26.What is the midpoint of the line joining (9, 6) and (11, 0)? (a) (3, 10) (b) (1, 3) (c) (10, 3) (d) (20, 6)
  27. 27.What is the distance between the points (7, 18) and (19, 2)? (a) 20 (b) 21 (c) 28 (d) 400
  28. 28.What is the distance between the points (2, 6) and (11, 18)? (a) 21 (b) 225 (c) 15 (d) 16
  29. 29.What is the distance between the points (8, 17) and (16, 2)? (a) 23 (b) 17 (c) 18 (d) 289
  30. 30.In which quadrant does the point (−7, −5) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  31. 31.In which quadrant does the point (3, 7) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  32. 32.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 23 (c) 18 (d) 17
  33. 33.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 14 (c) 13 (d) 17
  34. 34.What is the distance between the points (3, 8) and (15, 17)? (a) 16 (b) 15 (c) 225 (d) 21
  35. 35.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 14 (c) 11 (d) 100
  36. 36.What is the distance between the points (1, 2) and (10, 14)? (a) 21 (b) 16 (c) 15 (d) 225
  37. 37.What is the distance between the points (5, 1) and (10, 13)? (a) 14 (b) 17 (c) 13 (d) 169
  38. 38.What is the midpoint of the line joining (6, 11) and (10, 7)? (a) (2, 2) (b) (8, 9) (c) (9, 8) (d) (16, 18)
  39. 39.What is the distance between the points (2, 3) and (10, 9)? (a) 100 (b) 11 (c) 10 (d) 14
  40. 40.In which quadrant does the point (−1, −7) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant

Answer key

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

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