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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 249 · 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 (1, 2) and (5, 5)? (a) 7 (b) 25 (c) 5 (d) 6
  2. 2.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 225 (c) 16 (d) 15
  3. 3.What is the midpoint of the line joining (7, 10) and (13, 12)? (a) (10, 11) (b) (11, 10) (c) (20, 22) (d) (3, 1)
  4. 4.What is the distance between the points (2, 7) and (6, 4)? (a) 5 (b) 7 (c) 25 (d) 6
  5. 5.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 11 (c) 14 (d) 100
  6. 6.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 169 (c) 14 (d) 13
  7. 7.What is the distance between the points (4, 7) and (11, 31)? (a) 31 (b) 625 (c) 26 (d) 25
  8. 8.What is the midpoint of the line joining (8, 17) and (14, 5)? (a) (22, 22) (b) (3, 6) (c) (12, 11) (d) (11, 11)
  9. 9.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 21 (c) 15 (d) 16
  10. 10.In which quadrant does the point (−6, 1) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  11. 11.What is the midpoint of the line joining (5, 10) and (15, 18)? (a) (14, 10) (b) (10, 14) (c) (5, 4) (d) (20, 28)
  12. 12.What is the midpoint of the line joining (9, 3) and (19, 13)? (a) (5, 5) (b) (14, 8) (c) (8, 14) (d) (28, 16)
  13. 13.What is the midpoint of the line joining (4, 5) and (12, 11)? (a) (16, 16) (b) (9, 8) (c) (4, 3) (d) (8, 8)
  14. 14.What is the distance between the points (0, 13) and (3, 9)? (a) 7 (b) 5 (c) 25 (d) 6
  15. 15.What is the distance between the points (8, 8) and (23, 16)? (a) 18 (b) 289 (c) 17 (d) 23
  16. 16.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 20 (c) 28 (d) 400
  17. 17.What is the midpoint of the line joining (5, 5) and (7, 7)? (a) (7, 6) (b) (12, 12) (c) (6, 6) (d) (1, 1)
  18. 18.In which quadrant does the point (−2, 1) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  19. 19.What is the distance between the points (5, 7) and (8, 11)? (a) 25 (b) 5 (c) 7 (d) 6
  20. 20.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 26 (c) 25 (d) 31
  21. 21.How far is the point (12, 16) from the origin (0, 0)? (a) 20 (b) 28 (c) 21 (d) 400
  22. 22.In which quadrant does the point (8, −9) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  23. 23.What is the distance between the points (7, 0) and (19, 16)? (a) 400 (b) 21 (c) 28 (d) 20
  24. 24.What is the distance between the points (9, 8) and (16, 32)? (a) 25 (b) 26 (c) 625 (d) 31
  25. 25.What is the midpoint of the line joining (1, 5) and (9, 15)? (a) (4, 5) (b) (10, 5) (c) (5, 10) (d) (10, 20)
  26. 26.What is the distance between the points (6, 8) and (18, 3)? (a) 17 (b) 14 (c) 13 (d) 169
  27. 27.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 289 (c) 17 (d) 23
  28. 28.What is the midpoint of the line joining (9, 2) and (13, 8)? (a) (5, 11) (b) (2, 3) (c) (11, 5) (d) (22, 10)
  29. 29.What is the midpoint of the line joining (9, 11) and (11, 7)? (a) (9, 10) (b) (20, 18) (c) (1, 2) (d) (10, 9)
  30. 30.What is the midpoint of the line joining (2, 7) and (8, 3)? (a) (10, 10) (b) (5, 5) (c) (3, 2) (d) (6, 5)
  31. 31.In which quadrant does the point (−1, 4) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  32. 32.How far is the point (24, 7) from the origin (0, 0)? (a) 26 (b) 25 (c) 625 (d) 31
  33. 33.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 18 (c) 17 (d) 289
  34. 34.What is the distance between the points (9, 13) and (21, 8)? (a) 169 (b) 13 (c) 14 (d) 17
  35. 35.What is the midpoint of the line joining (3, 15) and (7, 5)? (a) (10, 5) (b) (10, 20) (c) (5, 10) (d) (2, 5)
  36. 36.What is the distance between the points (8, 8) and (32, 1)? (a) 31 (b) 625 (c) 26 (d) 25
  37. 37.In which quadrant does the point (−3, −8) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  38. 38.What is the distance between the points (1, 9) and (10, 21)? (a) 21 (b) 15 (c) 225 (d) 16
  39. 39.What is the midpoint of the line joining (2, 0) and (6, 12)? (a) (6, 4) (b) (8, 12) (c) (4, 6) (d) (2, 6)
  40. 40.In which quadrant does the point (7, 5) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant

Answer key

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

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