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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 547 · 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 (5, 12) from the origin (0, 0)? (a) 169 (b) 14 (c) 13 (d) 17
  2. 2.In which quadrant does the point (2, 9) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  3. 3.What is the distance between the points (0, 3) and (7, 27)? (a) 625 (b) 26 (c) 25 (d) 31
  4. 4.What is the midpoint of the line joining (3, 3) and (5, 15)? (a) (8, 18) (b) (1, 6) (c) (9, 4) (d) (4, 9)
  5. 5.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 18 (c) 289 (d) 17
  6. 6.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 17 (c) 289 (d) 18
  7. 7.In which quadrant does the point (7, 5) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  8. 8.What is the midpoint of the line joining (10, 3) and (16, 11)? (a) (3, 4) (b) (7, 13) (c) (13, 7) (d) (26, 14)
  9. 9.What is the distance between the points (0, 13) and (3, 9)? (a) 7 (b) 25 (c) 5 (d) 6
  10. 10.What is the distance between the points (1, 6) and (13, 11)? (a) 169 (b) 17 (c) 14 (d) 13
  11. 11.What is the midpoint of the line joining (1, 9) and (5, 1)? (a) (2, 4) (b) (5, 3) (c) (3, 5) (d) (6, 10)
  12. 12.How far is the point (12, 16) from the origin (0, 0)? (a) 20 (b) 400 (c) 28 (d) 21
  13. 13.What is the midpoint of the line joining (9, 9) and (15, 5)? (a) (7, 12) (b) (12, 7) (c) (24, 14) (d) (3, 2)
  14. 14.What is the distance between the points (0, 3) and (12, 8)? (a) 14 (b) 13 (c) 17 (d) 169
  15. 15.What is the midpoint of the line joining (9, 15) and (21, 9)? (a) (30, 24) (b) (6, 3) (c) (12, 15) (d) (15, 12)
  16. 16.What is the distance between the points (5, 1) and (14, 13)? (a) 16 (b) 15 (c) 21 (d) 225
  17. 17.What is the distance between the points (8, 5) and (23, 13)? (a) 18 (b) 23 (c) 17 (d) 289
  18. 18.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 21 (c) 225 (d) 15
  19. 19.In which quadrant does the point (−5, 4) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  20. 20.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 400 (c) 20 (d) 28
  21. 21.In which quadrant does the point (8, −2) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  22. 22.What is the distance between the points (4, 0) and (13, 12)? (a) 16 (b) 225 (c) 21 (d) 15
  23. 23.What is the midpoint of the line joining (8, 10) and (16, 20)? (a) (4, 5) (b) (24, 30) (c) (15, 12) (d) (12, 15)
  24. 24.What is the distance between the points (7, 4) and (14, 28)? (a) 31 (b) 26 (c) 625 (d) 25
  25. 25.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 26 (c) 31 (d) 25
  26. 26.In which quadrant does the point (−6, −1) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  27. 27.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 25 (c) 7 (d) 5
  28. 28.In which quadrant does the point (−6, 3) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  29. 29.What is the distance between the points (2, 3) and (9, 27)? (a) 625 (b) 31 (c) 25 (d) 26
  30. 30.What is the midpoint of the line joining (5, 10) and (15, 14)? (a) (20, 24) (b) (5, 2) (c) (10, 12) (d) (12, 10)
  31. 31.What is the distance between the points (0, 7) and (4, 10)? (a) 7 (b) 5 (c) 6 (d) 25
  32. 32.What is the distance between the points (7, 9) and (23, 21)? (a) 20 (b) 400 (c) 28 (d) 21
  33. 33.What is the midpoint of the line joining (0, 3) and (8, 7)? (a) (4, 2) (b) (8, 10) (c) (5, 4) (d) (4, 5)
  34. 34.What is the midpoint of the line joining (9, 10) and (11, 18)? (a) (14, 10) (b) (20, 28) (c) (1, 4) (d) (10, 14)
  35. 35.In which quadrant does the point (5, −9) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  36. 36.In which quadrant does the point (1, −4) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  37. 37.What is the distance between the points (1, 5) and (13, 0)? (a) 169 (b) 13 (c) 14 (d) 17
  38. 38.In which quadrant does the point (−3, −2) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  39. 39.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 25 (c) 6 (d) 5
  40. 40.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 10 (c) 11 (d) 100

Answer key

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

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