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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 43 · 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 (12, 9) from the origin (0, 0)? (a) 21 (b) 15 (c) 16 (d) 225
  2. 2.In which quadrant does the point (−6, 9) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  3. 3.What is the distance between the points (8, 6) and (16, 21)? (a) 289 (b) 23 (c) 17 (d) 18
  4. 4.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 23 (c) 17 (d) 18
  5. 5.In which quadrant does the point (−6, −1) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  6. 6.What is the distance between the points (4, 1) and (20, 13)? (a) 400 (b) 20 (c) 21 (d) 28
  7. 7.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 11 (c) 10 (d) 14
  8. 8.How far is the point (15, 8) from the origin (0, 0)? (a) 17 (b) 289 (c) 23 (d) 18
  9. 9.What is the midpoint of the line joining (4, 17) and (16, 7)? (a) (12, 10) (b) (6, 5) (c) (10, 12) (d) (20, 24)
  10. 10.What is the distance between the points (7, 2) and (22, 10)? (a) 289 (b) 18 (c) 17 (d) 23
  11. 11.In which quadrant does the point (−5, 7) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  12. 12.In which quadrant does the point (−4, 9) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  13. 13.What is the midpoint of the line joining (7, 0) and (19, 8)? (a) (6, 4) (b) (13, 4) (c) (26, 8) (d) (4, 13)
  14. 14.What is the midpoint of the line joining (10, 7) and (22, 9)? (a) (6, 1) (b) (32, 16) (c) (16, 8) (d) (8, 16)
  15. 15.What is the distance between the points (3, 2) and (9, 10)? (a) 10 (b) 100 (c) 14 (d) 11
  16. 16.What is the midpoint of the line joining (3, 9) and (11, 3)? (a) (7, 6) (b) (4, 3) (c) (14, 12) (d) (6, 7)
  17. 17.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 21 (c) 400 (d) 28
  18. 18.What is the distance between the points (9, 9) and (17, 15)? (a) 14 (b) 11 (c) 10 (d) 100
  19. 19.What is the distance between the points (5, 7) and (12, 31)? (a) 31 (b) 26 (c) 625 (d) 25
  20. 20.In which quadrant does the point (3, 7) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  21. 21.What is the distance between the points (0, 8) and (9, 20)? (a) 21 (b) 225 (c) 16 (d) 15
  22. 22.What is the distance between the points (9, 16) and (15, 8)? (a) 100 (b) 11 (c) 10 (d) 14
  23. 23.What is the distance between the points (2, 2) and (14, 18)? (a) 400 (b) 21 (c) 20 (d) 28
  24. 24.In which quadrant does the point (−4, −5) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  25. 25.In which quadrant does the point (8, −8) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  26. 26.What is the distance between the points (1, 11) and (9, 5)? (a) 11 (b) 100 (c) 14 (d) 10
  27. 27.What is the distance between the points (9, 7) and (13, 10)? (a) 7 (b) 5 (c) 6 (d) 25
  28. 28.What is the distance between the points (3, 1) and (15, 10)? (a) 21 (b) 16 (c) 225 (d) 15
  29. 29.What is the distance between the points (3, 0) and (15, 5)? (a) 13 (b) 17 (c) 169 (d) 14
  30. 30.What is the distance between the points (6, 24) and (13, 0)? (a) 625 (b) 26 (c) 31 (d) 25
  31. 31.How far is the point (7, 24) from the origin (0, 0)? (a) 25 (b) 625 (c) 26 (d) 31
  32. 32.How far is the point (12, 16) from the origin (0, 0)? (a) 20 (b) 21 (c) 28 (d) 400
  33. 33.What is the midpoint of the line joining (5, 12) and (13, 8)? (a) (9, 10) (b) (10, 9) (c) (4, 2) (d) (18, 20)
  34. 34.In which quadrant does the point (1, 5) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  35. 35.What is the distance between the points (9, 12) and (33, 5)? (a) 26 (b) 625 (c) 25 (d) 31
  36. 36.What is the distance between the points (2, 4) and (17, 12)? (a) 289 (b) 18 (c) 17 (d) 23
  37. 37.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 7 (c) 5 (d) 6
  38. 38.What is the distance between the points (7, 14) and (15, 8)? (a) 100 (b) 10 (c) 11 (d) 14
  39. 39.In which quadrant does the point (−3, 1) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  40. 40.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 7 (c) 5 (d) 6

Answer key

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

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