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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 921 · 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, −8) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  2. 2.What is the midpoint of the line joining (7, 7) and (15, 5)? (a) (4, 1) (b) (11, 6) (c) (22, 12) (d) (6, 11)
  3. 3.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 13 (c) 169 (d) 14
  4. 4.In which quadrant does the point (1, 9) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  5. 5.What is the midpoint of the line joining (6, 4) and (12, 14)? (a) (3, 5) (b) (10, 9) (c) (18, 18) (d) (9, 9)
  6. 6.What is the midpoint of the line joining (3, 4) and (7, 12)? (a) (8, 5) (b) (5, 8) (c) (10, 16) (d) (2, 4)
  7. 7.What is the distance between the points (6, 9) and (14, 24)? (a) 17 (b) 18 (c) 23 (d) 289
  8. 8.What is the midpoint of the line joining (5, 12) and (7, 0)? (a) (12, 12) (b) (7, 6) (c) (6, 6) (d) (1, 6)
  9. 9.How far is the point (24, 7) from the origin (0, 0)? (a) 26 (b) 25 (c) 625 (d) 31
  10. 10.What is the midpoint of the line joining (4, 6) and (6, 18)? (a) (12, 5) (b) (1, 6) (c) (10, 24) (d) (5, 12)
  11. 11.What is the distance between the points (5, 13) and (14, 1)? (a) 21 (b) 225 (c) 15 (d) 16
  12. 12.What is the distance between the points (1, 9) and (10, 21)? (a) 225 (b) 15 (c) 16 (d) 21
  13. 13.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 25 (c) 5 (d) 6
  14. 14.What is the midpoint of the line joining (1, 8) and (5, 20)? (a) (6, 28) (b) (2, 6) (c) (3, 14) (d) (14, 3)
  15. 15.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 14 (c) 100 (d) 10
  16. 16.What is the distance between the points (6, 9) and (18, 25)? (a) 400 (b) 28 (c) 21 (d) 20
  17. 17.What is the midpoint of the line joining (7, 15) and (17, 7)? (a) (5, 4) (b) (11, 12) (c) (12, 11) (d) (24, 22)
  18. 18.What is the distance between the points (7, 2) and (14, 26)? (a) 25 (b) 26 (c) 625 (d) 31
  19. 19.What is the midpoint of the line joining (7, 9) and (19, 21)? (a) (15, 13) (b) (26, 30) (c) (13, 15) (d) (6, 6)
  20. 20.What is the midpoint of the line joining (1, 2) and (11, 4)? (a) (5, 1) (b) (3, 6) (c) (12, 6) (d) (6, 3)
  21. 21.What is the distance between the points (4, 7) and (11, 31)? (a) 26 (b) 31 (c) 625 (d) 25
  22. 22.What is the midpoint of the line joining (8, 12) and (10, 10)? (a) (18, 22) (b) (1, 1) (c) (9, 11) (d) (11, 9)
  23. 23.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 21 (c) 20 (d) 400
  24. 24.What is the midpoint of the line joining (8, 13) and (10, 1)? (a) (1, 6) (b) (18, 14) (c) (7, 9) (d) (9, 7)
  25. 25.What is the midpoint of the line joining (3, 17) and (7, 7)? (a) (10, 24) (b) (12, 5) (c) (2, 5) (d) (5, 12)
  26. 26.What is the midpoint of the line joining (3, 8) and (7, 12)? (a) (2, 2) (b) (10, 20) (c) (10, 5) (d) (5, 10)
  27. 27.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 289 (c) 17 (d) 23
  28. 28.In which quadrant does the point (−6, −9) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  29. 29.In which quadrant does the point (8, 3) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  30. 30.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 23 (c) 17 (d) 18
  31. 31.What is the midpoint of the line joining (10, 7) and (14, 9)? (a) (24, 16) (b) (8, 12) (c) (2, 1) (d) (12, 8)
  32. 32.In which quadrant does the point (2, 2) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  33. 33.What is the midpoint of the line joining (5, 11) and (15, 7)? (a) (5, 2) (b) (9, 10) (c) (20, 18) (d) (10, 9)
  34. 34.What is the midpoint of the line joining (5, 6) and (13, 18)? (a) (4, 6) (b) (12, 9) (c) (9, 12) (d) (18, 24)
  35. 35.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 21 (c) 28 (d) 20
  36. 36.What is the distance between the points (6, 6) and (18, 15)? (a) 16 (b) 21 (c) 15 (d) 225
  37. 37.In which quadrant does the point (1, 5) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  38. 38.In which quadrant does the point (−1, 8) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  39. 39.What is the distance between the points (9, 16) and (33, 9)? (a) 625 (b) 26 (c) 25 (d) 31
  40. 40.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 16 (c) 225 (d) 15

Answer key

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

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