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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 767 · 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.In which quadrant does the point (3, −7) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  2. 2.What is the midpoint of the line joining (2, 3) and (14, 11)? (a) (16, 14) (b) (6, 4) (c) (8, 7) (d) (7, 8)
  3. 3.What is the midpoint of the line joining (7, 4) and (13, 16)? (a) (11, 10) (b) (3, 6) (c) (20, 20) (d) (10, 10)
  4. 4.What is the distance between the points (1, 6) and (9, 12)? (a) 14 (b) 11 (c) 100 (d) 10
  5. 5.What is the midpoint of the line joining (1, 6) and (11, 2)? (a) (4, 6) (b) (5, 2) (c) (12, 8) (d) (6, 4)
  6. 6.In which quadrant does the point (7, 2) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  7. 7.What is the distance between the points (1, 14) and (25, 7)? (a) 26 (b) 625 (c) 25 (d) 31
  8. 8.What is the distance between the points (4, 3) and (28, 10)? (a) 25 (b) 625 (c) 26 (d) 31
  9. 9.What is the midpoint of the line joining (4, 7) and (12, 11)? (a) (8, 9) (b) (16, 18) (c) (4, 2) (d) (9, 8)
  10. 10.What is the midpoint of the line joining (7, 3) and (13, 15)? (a) (20, 18) (b) (3, 6) (c) (10, 9) (d) (9, 10)
  11. 11.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 13 (c) 169 (d) 14
  12. 12.What is the midpoint of the line joining (9, 1) and (19, 9)? (a) (14, 5) (b) (5, 4) (c) (28, 10) (d) (5, 14)
  13. 13.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 289 (c) 18 (d) 23
  14. 14.In which quadrant does the point (4, 6) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  15. 15.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 25 (c) 5 (d) 7
  16. 16.What is the distance between the points (8, 10) and (16, 4)? (a) 100 (b) 14 (c) 11 (d) 10
  17. 17.What is the distance between the points (7, 12) and (12, 0)? (a) 169 (b) 14 (c) 17 (d) 13
  18. 18.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 14 (c) 10 (d) 11
  19. 19.What is the distance between the points (9, 9) and (12, 13)? (a) 7 (b) 25 (c) 5 (d) 6
  20. 20.What is the midpoint of the line joining (10, 14) and (20, 2)? (a) (30, 16) (b) (8, 15) (c) (15, 8) (d) (5, 6)
  21. 21.What is the midpoint of the line joining (2, 12) and (10, 2)? (a) (7, 6) (b) (12, 14) (c) (4, 5) (d) (6, 7)
  22. 22.What is the distance between the points (0, 12) and (24, 5)? (a) 625 (b) 26 (c) 25 (d) 31
  23. 23.What is the distance between the points (3, 9) and (9, 1)? (a) 100 (b) 11 (c) 10 (d) 14
  24. 24.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 225 (c) 15 (d) 16
  25. 25.What is the midpoint of the line joining (1, 0) and (5, 10)? (a) (2, 5) (b) (3, 5) (c) (6, 10) (d) (5, 3)
  26. 26.What is the midpoint of the line joining (0, 12) and (4, 0)? (a) (3, 6) (b) (6, 2) (c) (2, 6) (d) (4, 12)
  27. 27.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 625 (c) 25 (d) 31
  28. 28.What is the midpoint of the line joining (10, 8) and (22, 16)? (a) (6, 4) (b) (12, 16) (c) (32, 24) (d) (16, 12)
  29. 29.In which quadrant does the point (−2, 2) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  30. 30.What is the midpoint of the line joining (2, 14) and (10, 10)? (a) (4, 2) (b) (12, 6) (c) (12, 24) (d) (6, 12)
  31. 31.What is the midpoint of the line joining (0, 7) and (4, 9)? (a) (4, 16) (b) (8, 2) (c) (2, 8) (d) (2, 1)
  32. 32.What is the midpoint of the line joining (9, 2) and (11, 10)? (a) (10, 6) (b) (1, 4) (c) (6, 10) (d) (20, 12)
  33. 33.What is the midpoint of the line joining (8, 3) and (12, 1)? (a) (2, 1) (b) (20, 4) (c) (10, 2) (d) (2, 10)
  34. 34.What is the midpoint of the line joining (1, 13) and (9, 7)? (a) (5, 10) (b) (10, 20) (c) (4, 3) (d) (10, 5)
  35. 35.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 14 (c) 100 (d) 11
  36. 36.What is the distance between the points (1, 4) and (4, 0)? (a) 6 (b) 7 (c) 25 (d) 5
  37. 37.What is the distance between the points (3, 10) and (6, 6)? (a) 5 (b) 25 (c) 7 (d) 6
  38. 38.What is the midpoint of the line joining (9, 13) and (21, 1)? (a) (6, 6) (b) (15, 7) (c) (7, 15) (d) (30, 14)
  39. 39.What is the distance between the points (4, 9) and (11, 33)? (a) 31 (b) 25 (c) 26 (d) 625
  40. 40.What is the distance between the points (1, 8) and (6, 20)? (a) 169 (b) 13 (c) 17 (d) 14

Answer key

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

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