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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 411 · 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.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 21 (c) 16 (d) 15
  2. 2.What is the midpoint of the line joining (6, 11) and (14, 3)? (a) (20, 14) (b) (4, 4) (c) (10, 7) (d) (7, 10)
  3. 3.What is the distance between the points (0, 0) and (8, 6)? (a) 11 (b) 14 (c) 100 (d) 10
  4. 4.What is the midpoint of the line joining (6, 9) and (10, 11)? (a) (10, 8) (b) (16, 20) (c) (2, 1) (d) (8, 10)
  5. 5.What is the midpoint of the line joining (0, 4) and (2, 12)? (a) (2, 16) (b) (8, 1) (c) (1, 4) (d) (1, 8)
  6. 6.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 23 (c) 289 (d) 18
  7. 7.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 16 (c) 225 (d) 15
  8. 8.What is the distance between the points (9, 5) and (18, 17)? (a) 15 (b) 225 (c) 21 (d) 16
  9. 9.What is the distance between the points (9, 4) and (13, 1)? (a) 6 (b) 7 (c) 25 (d) 5
  10. 10.In which quadrant does the point (−9, 6) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  11. 11.What is the distance between the points (8, 11) and (11, 7)? (a) 7 (b) 6 (c) 25 (d) 5
  12. 12.In which quadrant does the point (−7, −9) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  13. 13.What is the midpoint of the line joining (9, 6) and (21, 2)? (a) (4, 15) (b) (6, 2) (c) (30, 8) (d) (15, 4)
  14. 14.What is the distance between the points (6, 22) and (18, 6)? (a) 21 (b) 20 (c) 28 (d) 400
  15. 15.What is the midpoint of the line joining (0, 6) and (2, 2)? (a) (1, 2) (b) (1, 4) (c) (2, 8) (d) (4, 1)
  16. 16.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 25 (c) 6 (d) 5
  17. 17.In which quadrant does the point (−3, −5) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  18. 18.What is the distance between the points (0, 24) and (7, 0)? (a) 26 (b) 25 (c) 625 (d) 31
  19. 19.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 625 (c) 25 (d) 26
  20. 20.In which quadrant does the point (4, 6) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  21. 21.What is the midpoint of the line joining (8, 14) and (20, 4)? (a) (6, 5) (b) (28, 18) (c) (9, 14) (d) (14, 9)
  22. 22.What is the distance between the points (3, 2) and (9, 10)? (a) 14 (b) 100 (c) 10 (d) 11
  23. 23.What is the midpoint of the line joining (0, 8) and (4, 2)? (a) (4, 10) (b) (2, 5) (c) (2, 3) (d) (5, 2)
  24. 24.In which quadrant does the point (3, 4) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  25. 25.In which quadrant does the point (−5, 2) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  26. 26.What is the midpoint of the line joining (6, 1) and (12, 13)? (a) (7, 9) (b) (18, 14) (c) (3, 6) (d) (9, 7)
  27. 27.What is the midpoint of the line joining (8, 0) and (12, 12)? (a) (6, 10) (b) (10, 6) (c) (2, 6) (d) (20, 12)
  28. 28.What is the midpoint of the line joining (3, 0) and (13, 4)? (a) (2, 8) (b) (16, 4) (c) (5, 2) (d) (8, 2)
  29. 29.In which quadrant does the point (4, 7) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  30. 30.What is the midpoint of the line joining (3, 20) and (5, 10)? (a) (15, 4) (b) (4, 15) (c) (8, 30) (d) (1, 5)
  31. 31.What is the distance between the points (9, 8) and (13, 11)? (a) 25 (b) 6 (c) 7 (d) 5
  32. 32.What is the midpoint of the line joining (0, 12) and (8, 8)? (a) (10, 4) (b) (4, 2) (c) (8, 20) (d) (4, 10)
  33. 33.In which quadrant does the point (2, −1) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  34. 34.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 169 (c) 14 (d) 13
  35. 35.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 20 (c) 400 (d) 21
  36. 36.What is the midpoint of the line joining (9, 10) and (17, 16)? (a) (26, 26) (b) (13, 13) (c) (4, 3) (d) (14, 13)
  37. 37.What is the distance between the points (3, 23) and (11, 8)? (a) 18 (b) 289 (c) 23 (d) 17
  38. 38.What is the midpoint of the line joining (1, 4) and (7, 14)? (a) (4, 9) (b) (9, 4) (c) (3, 5) (d) (8, 18)
  39. 39.In which quadrant does the point (2, 8) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  40. 40.In which quadrant does the point (−8, 5) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant

Answer key

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

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