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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 850 · 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, 20) and (12, 8)? (a) 13 (b) 14 (c) 169 (d) 17
  2. 2.In which quadrant does the point (6, 4) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  3. 3.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 14 (c) 100 (d) 11
  4. 4.In which quadrant does the point (−3, −7) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  5. 5.What is the midpoint of the line joining (3, 2) and (7, 8)? (a) (5, 5) (b) (10, 10) (c) (2, 3) (d) (6, 5)
  6. 6.In which quadrant does the point (−9, −3) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  7. 7.What is the midpoint of the line joining (1, 21) and (5, 9)? (a) (15, 3) (b) (2, 6) (c) (6, 30) (d) (3, 15)
  8. 8.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 26 (c) 25 (d) 625
  9. 9.What is the distance between the points (5, 8) and (9, 11)? (a) 7 (b) 25 (c) 5 (d) 6
  10. 10.In which quadrant does the point (1, 4) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  11. 11.In which quadrant does the point (3, −7) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  12. 12.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 28 (c) 20 (d) 21
  13. 13.What is the midpoint of the line joining (5, 0) and (9, 4)? (a) (14, 4) (b) (2, 2) (c) (7, 2) (d) (2, 7)
  14. 14.What is the distance between the points (2, 8) and (8, 0)? (a) 100 (b) 11 (c) 10 (d) 14
  15. 15.What is the midpoint of the line joining (10, 10) and (22, 22)? (a) (6, 6) (b) (32, 32) (c) (17, 16) (d) (16, 16)
  16. 16.In which quadrant does the point (9, −8) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  17. 17.What is the midpoint of the line joining (3, 8) and (9, 0)? (a) (3, 4) (b) (4, 6) (c) (6, 4) (d) (12, 8)
  18. 18.What is the midpoint of the line joining (9, 11) and (19, 7)? (a) (9, 14) (b) (14, 9) (c) (5, 2) (d) (28, 18)
  19. 19.What is the distance between the points (4, 5) and (16, 14)? (a) 225 (b) 16 (c) 21 (d) 15
  20. 20.What is the midpoint of the line joining (2, 4) and (12, 16)? (a) (14, 20) (b) (7, 10) (c) (10, 7) (d) (5, 6)
  21. 21.In which quadrant does the point (2, 3) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  22. 22.What is the distance between the points (9, 3) and (12, 7)? (a) 6 (b) 7 (c) 5 (d) 25
  23. 23.In which quadrant does the point (3, −6) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  24. 24.In which quadrant does the point (−7, −2) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  25. 25.In which quadrant does the point (−6, −9) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  26. 26.What is the distance between the points (1, 5) and (9, 20)? (a) 23 (b) 289 (c) 18 (d) 17
  27. 27.What is the distance between the points (3, 2) and (10, 26)? (a) 31 (b) 26 (c) 25 (d) 625
  28. 28.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 7 (c) 5 (d) 25
  29. 29.What is the distance between the points (0, 5) and (3, 1)? (a) 5 (b) 7 (c) 25 (d) 6
  30. 30.What is the midpoint of the line joining (8, 4) and (20, 2)? (a) (28, 6) (b) (14, 3) (c) (6, 1) (d) (3, 14)
  31. 31.What is the distance between the points (0, 16) and (12, 0)? (a) 400 (b) 20 (c) 28 (d) 21
  32. 32.In which quadrant does the point (−2, −8) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  33. 33.In which quadrant does the point (5, 1) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  34. 34.What is the distance between the points (0, 16) and (24, 9)? (a) 25 (b) 31 (c) 625 (d) 26
  35. 35.What is the distance between the points (9, 17) and (17, 2)? (a) 18 (b) 289 (c) 23 (d) 17
  36. 36.What is the distance between the points (0, 5) and (12, 14)? (a) 16 (b) 225 (c) 15 (d) 21
  37. 37.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 17 (c) 13 (d) 169
  38. 38.What is the midpoint of the line joining (7, 1) and (9, 3)? (a) (8, 2) (b) (16, 4) (c) (2, 8) (d) (1, 1)
  39. 39.What is the distance between the points (9, 20) and (25, 8)? (a) 400 (b) 28 (c) 21 (d) 20
  40. 40.What is the distance between the points (2, 3) and (7, 15)? (a) 14 (b) 169 (c) 13 (d) 17

Answer key

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

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