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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 672 · 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.What is the distance between the points (7, 13) and (16, 1)? (a) 16 (b) 225 (c) 21 (d) 15
  2. 2.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 15 (c) 21 (d) 16
  3. 3.What is the distance between the points (2, 8) and (14, 24)? (a) 21 (b) 28 (c) 20 (d) 400
  4. 4.In which quadrant does the point (−1, 2) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  5. 5.In which quadrant does the point (7, 1) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  6. 6.In which quadrant does the point (2, 6) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  7. 7.What is the midpoint of the line joining (7, 5) and (17, 15)? (a) (24, 20) (b) (10, 12) (c) (12, 10) (d) (5, 5)
  8. 8.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 169 (c) 17 (d) 13
  9. 9.In which quadrant does the point (−5, −3) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  10. 10.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 18 (c) 17 (d) 23
  11. 11.In which quadrant does the point (2, 2) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  12. 12.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 18 (c) 23 (d) 289
  13. 13.What is the distance between the points (2, 11) and (14, 6)? (a) 13 (b) 169 (c) 14 (d) 17
  14. 14.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 21 (c) 16 (d) 15
  15. 15.In which quadrant does the point (4, 8) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  16. 16.What is the distance between the points (9, 14) and (25, 2)? (a) 400 (b) 21 (c) 20 (d) 28
  17. 17.What is the distance between the points (4, 1) and (12, 7)? (a) 11 (b) 14 (c) 100 (d) 10
  18. 18.What is the distance between the points (6, 6) and (30, 13)? (a) 625 (b) 25 (c) 31 (d) 26
  19. 19.What is the midpoint of the line joining (4, 12) and (14, 0)? (a) (6, 9) (b) (18, 12) (c) (9, 6) (d) (5, 6)
  20. 20.In which quadrant does the point (−3, −6) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  21. 21.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 11 (c) 100 (d) 14
  22. 22.How far is the point (24, 7) from the origin (0, 0)? (a) 26 (b) 625 (c) 31 (d) 25
  23. 23.What is the midpoint of the line joining (9, 22) and (21, 10)? (a) (30, 32) (b) (15, 16) (c) (16, 15) (d) (6, 6)
  24. 24.What is the distance between the points (0, 2) and (8, 17)? (a) 18 (b) 289 (c) 17 (d) 23
  25. 25.What is the distance between the points (9, 17) and (14, 5)? (a) 14 (b) 169 (c) 13 (d) 17
  26. 26.In which quadrant does the point (−7, 8) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  27. 27.What is the midpoint of the line joining (4, 18) and (10, 8)? (a) (3, 5) (b) (7, 13) (c) (13, 7) (d) (14, 26)
  28. 28.What is the distance between the points (5, 28) and (12, 4)? (a) 26 (b) 625 (c) 31 (d) 25
  29. 29.What is the distance between the points (1, 23) and (9, 8)? (a) 289 (b) 18 (c) 17 (d) 23
  30. 30.What is the distance between the points (7, 14) and (19, 9)? (a) 14 (b) 13 (c) 169 (d) 17
  31. 31.In which quadrant does the point (2, 7) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  32. 32.In which quadrant does the point (−6, 4) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  33. 33.In which quadrant does the point (−9, 2) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  34. 34.In which quadrant does the point (−8, −1) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  35. 35.What is the midpoint of the line joining (8, 18) and (10, 8)? (a) (18, 26) (b) (9, 13) (c) (1, 5) (d) (13, 9)
  36. 36.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 17 (c) 14 (d) 13
  37. 37.In which quadrant does the point (3, 6) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  38. 38.In which quadrant does the point (−9, 5) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  39. 39.In which quadrant does the point (3, 2) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  40. 40.What is the distance between the points (8, 4) and (32, 11)? (a) 625 (b) 25 (c) 31 (d) 26

Answer key

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

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