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Coordinate Geometry Worksheet for Maths Olympiad

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

Answer key

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

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