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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 514 · 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 (8, 6) from the origin (0, 0)? (a) 11 (b) 14 (c) 100 (d) 10
  2. 2.What is the distance between the points (4, 17) and (9, 5)? (a) 169 (b) 14 (c) 17 (d) 13
  3. 3.What is the midpoint of the line joining (1, 8) and (9, 18)? (a) (10, 26) (b) (4, 5) (c) (13, 5) (d) (5, 13)
  4. 4.What is the midpoint of the line joining (7, 2) and (17, 12)? (a) (7, 12) (b) (5, 5) (c) (12, 7) (d) (24, 14)
  5. 5.In which quadrant does the point (2, −7) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  6. 6.What is the distance between the points (3, 5) and (7, 8)? (a) 5 (b) 25 (c) 7 (d) 6
  7. 7.In which quadrant does the point (−1, 3) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  8. 8.What is the midpoint of the line joining (2, 10) and (6, 16)? (a) (13, 4) (b) (2, 3) (c) (8, 26) (d) (4, 13)
  9. 9.In which quadrant does the point (−1, 8) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  10. 10.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 11 (c) 14 (d) 10
  11. 11.In which quadrant does the point (−1, −5) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  12. 12.What is the midpoint of the line joining (5, 0) and (7, 6)? (a) (12, 6) (b) (6, 3) (c) (1, 3) (d) (3, 6)
  13. 13.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 25 (c) 5 (d) 6
  14. 14.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 28 (c) 20 (d) 400
  15. 15.What is the midpoint of the line joining (9, 1) and (11, 3)? (a) (2, 10) (b) (1, 1) (c) (10, 2) (d) (20, 4)
  16. 16.In which quadrant does the point (5, 5) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  17. 17.What is the midpoint of the line joining (6, 3) and (10, 9)? (a) (2, 3) (b) (6, 8) (c) (16, 12) (d) (8, 6)
  18. 18.In which quadrant does the point (−6, 2) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  19. 19.What is the midpoint of the line joining (7, 2) and (17, 10)? (a) (24, 12) (b) (5, 4) (c) (6, 12) (d) (12, 6)
  20. 20.What is the distance between the points (0, 17) and (9, 5)? (a) 21 (b) 15 (c) 225 (d) 16
  21. 21.What is the distance between the points (9, 5) and (25, 17)? (a) 20 (b) 21 (c) 400 (d) 28
  22. 22.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 15 (c) 16 (d) 225
  23. 23.In which quadrant does the point (1, 6) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  24. 24.What is the midpoint of the line joining (2, 4) and (8, 8)? (a) (5, 6) (b) (6, 5) (c) (3, 2) (d) (10, 12)
  25. 25.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 23 (c) 289 (d) 18
  26. 26.What is the midpoint of the line joining (2, 10) and (14, 4)? (a) (6, 3) (b) (7, 8) (c) (8, 7) (d) (16, 14)
  27. 27.In which quadrant does the point (−3, −1) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  28. 28.What is the midpoint of the line joining (1, 14) and (11, 10)? (a) (5, 2) (b) (12, 6) (c) (12, 24) (d) (6, 12)
  29. 29.What is the distance between the points (7, 16) and (19, 0)? (a) 400 (b) 21 (c) 20 (d) 28
  30. 30.What is the midpoint of the line joining (5, 10) and (15, 4)? (a) (7, 10) (b) (20, 14) (c) (10, 7) (d) (5, 3)
  31. 31.What is the distance between the points (1, 1) and (25, 8)? (a) 31 (b) 26 (c) 625 (d) 25
  32. 32.What is the midpoint of the line joining (2, 8) and (4, 18)? (a) (6, 26) (b) (3, 13) (c) (1, 5) (d) (13, 3)
  33. 33.What is the midpoint of the line joining (10, 8) and (18, 12)? (a) (4, 2) (b) (14, 10) (c) (10, 14) (d) (28, 20)
  34. 34.What is the distance between the points (1, 2) and (9, 8)? (a) 100 (b) 11 (c) 14 (d) 10
  35. 35.In which quadrant does the point (−1, −6) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  36. 36.In which quadrant does the point (5, 9) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  37. 37.What is the midpoint of the line joining (1, 16) and (3, 6)? (a) (4, 22) (b) (11, 2) (c) (2, 11) (d) (1, 5)
  38. 38.What is the midpoint of the line joining (0, 10) and (4, 12)? (a) (2, 1) (b) (11, 2) (c) (2, 11) (d) (4, 22)
  39. 39.What is the distance between the points (4, 20) and (13, 8)? (a) 21 (b) 15 (c) 225 (d) 16
  40. 40.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 14 (c) 13 (d) 169

Answer key

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

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