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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 363 · 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 (24, 7) from the origin (0, 0)? (a) 31 (b) 625 (c) 26 (d) 25
  2. 2.In which quadrant does the point (−5, 8) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  3. 3.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 100 (c) 10 (d) 14
  4. 4.In which quadrant does the point (−5, −4) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  5. 5.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 16 (c) 15 (d) 225
  6. 6.How far is the point (12, 5) from the origin (0, 0)? (a) 13 (b) 17 (c) 169 (d) 14
  7. 7.In which quadrant does the point (1, 4) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  8. 8.What is the distance between the points (2, 5) and (9, 29)? (a) 26 (b) 31 (c) 25 (d) 625
  9. 9.What is the distance between the points (4, 6) and (10, 14)? (a) 14 (b) 10 (c) 11 (d) 100
  10. 10.What is the midpoint of the line joining (2, 17) and (14, 9)? (a) (13, 8) (b) (8, 13) (c) (16, 26) (d) (6, 4)
  11. 11.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 20 (c) 400 (d) 28
  12. 12.What is the distance between the points (2, 7) and (10, 1)? (a) 10 (b) 14 (c) 100 (d) 11
  13. 13.What is the midpoint of the line joining (7, 1) and (11, 3)? (a) (9, 2) (b) (2, 1) (c) (2, 9) (d) (18, 4)
  14. 14.What is the midpoint of the line joining (1, 0) and (13, 8)? (a) (14, 8) (b) (7, 4) (c) (4, 7) (d) (6, 4)
  15. 15.What is the midpoint of the line joining (5, 8) and (17, 18)? (a) (6, 5) (b) (13, 11) (c) (11, 13) (d) (22, 26)
  16. 16.In which quadrant does the point (7, 3) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  17. 17.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 6 (c) 25 (d) 5
  18. 18.In which quadrant does the point (−8, −9) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  19. 19.What is the distance between the points (8, 2) and (20, 18)? (a) 400 (b) 21 (c) 20 (d) 28
  20. 20.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 23 (c) 289 (d) 17
  21. 21.What is the distance between the points (1, 8) and (5, 11)? (a) 6 (b) 5 (c) 25 (d) 7
  22. 22.In which quadrant does the point (−8, 4) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  23. 23.What is the midpoint of the line joining (2, 5) and (8, 1)? (a) (10, 6) (b) (3, 2) (c) (5, 3) (d) (3, 5)
  24. 24.What is the midpoint of the line joining (8, 0) and (10, 2)? (a) (1, 9) (b) (9, 1) (c) (1, 1) (d) (18, 2)
  25. 25.What is the distance between the points (4, 15) and (12, 0)? (a) 18 (b) 17 (c) 23 (d) 289
  26. 26.What is the distance between the points (6, 6) and (21, 14)? (a) 23 (b) 18 (c) 289 (d) 17
  27. 27.What is the distance between the points (8, 18) and (20, 2)? (a) 400 (b) 21 (c) 28 (d) 20
  28. 28.In which quadrant does the point (−5, −1) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  29. 29.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 15 (c) 16 (d) 225
  30. 30.What is the midpoint of the line joining (1, 10) and (13, 6)? (a) (14, 16) (b) (7, 8) (c) (8, 7) (d) (6, 2)
  31. 31.What is the distance between the points (3, 10) and (6, 6)? (a) 5 (b) 6 (c) 25 (d) 7
  32. 32.What is the midpoint of the line joining (8, 10) and (14, 20)? (a) (15, 11) (b) (22, 30) (c) (3, 5) (d) (11, 15)
  33. 33.What is the midpoint of the line joining (5, 11) and (9, 9)? (a) (14, 20) (b) (10, 7) (c) (2, 1) (d) (7, 10)
  34. 34.What is the distance between the points (4, 1) and (7, 5)? (a) 7 (b) 25 (c) 6 (d) 5
  35. 35.What is the distance between the points (9, 8) and (33, 15)? (a) 25 (b) 26 (c) 625 (d) 31
  36. 36.In which quadrant does the point (−4, −6) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  37. 37.What is the distance between the points (1, 9) and (9, 3)? (a) 14 (b) 10 (c) 100 (d) 11
  38. 38.In which quadrant does the point (1, 9) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  39. 39.What is the midpoint of the line joining (3, 7) and (9, 5)? (a) (6, 6) (b) (3, 1) (c) (12, 12) (d) (7, 6)
  40. 40.What is the distance between the points (7, 5) and (13, 13)? (a) 11 (b) 100 (c) 14 (d) 10

Answer key

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

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