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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 174 · 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 (4, 3) from the origin (0, 0)? (a) 25 (b) 6 (c) 7 (d) 5
  2. 2.What is the distance between the points (3, 12) and (9, 4)? (a) 100 (b) 11 (c) 14 (d) 10
  3. 3.In which quadrant does the point (−2, 7) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  4. 4.In which quadrant does the point (−3, −5) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  5. 5.What is the midpoint of the line joining (7, 2) and (19, 0)? (a) (1, 13) (b) (26, 2) (c) (6, 1) (d) (13, 1)
  6. 6.What is the distance between the points (8, 14) and (20, 5)? (a) 16 (b) 21 (c) 15 (d) 225
  7. 7.How far is the point (9, 12) from the origin (0, 0)? (a) 15 (b) 225 (c) 16 (d) 21
  8. 8.In which quadrant does the point (−7, 9) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  9. 9.What is the distance between the points (9, 14) and (17, 8)? (a) 14 (b) 11 (c) 10 (d) 100
  10. 10.What is the distance between the points (7, 1) and (14, 25)? (a) 625 (b) 25 (c) 26 (d) 31
  11. 11.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 20 (c) 400 (d) 21
  12. 12.What is the midpoint of the line joining (7, 6) and (19, 0)? (a) (13, 3) (b) (3, 13) (c) (26, 6) (d) (6, 3)
  13. 13.What is the midpoint of the line joining (4, 12) and (10, 2)? (a) (8, 7) (b) (3, 5) (c) (14, 14) (d) (7, 7)
  14. 14.In which quadrant does the point (−9, 1) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  15. 15.What is the midpoint of the line joining (7, 15) and (9, 7)? (a) (16, 22) (b) (1, 4) (c) (11, 8) (d) (8, 11)
  16. 16.What is the midpoint of the line joining (0, 15) and (8, 3)? (a) (8, 18) (b) (4, 6) (c) (4, 9) (d) (9, 4)
  17. 17.In which quadrant does the point (6, 6) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  18. 18.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 17 (c) 289 (d) 23
  19. 19.What is the distance between the points (0, 4) and (8, 19)? (a) 23 (b) 289 (c) 18 (d) 17
  20. 20.In which quadrant does the point (9, −2) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  21. 21.What is the midpoint of the line joining (2, 2) and (12, 8)? (a) (7, 5) (b) (5, 3) (c) (5, 7) (d) (14, 10)
  22. 22.What is the midpoint of the line joining (6, 2) and (14, 10)? (a) (6, 10) (b) (20, 12) (c) (4, 4) (d) (10, 6)
  23. 23.What is the distance between the points (9, 10) and (33, 3)? (a) 625 (b) 26 (c) 31 (d) 25
  24. 24.What is the midpoint of the line joining (2, 9) and (8, 17)? (a) (13, 5) (b) (3, 4) (c) (5, 13) (d) (10, 26)
  25. 25.What is the distance between the points (3, 1) and (18, 9)? (a) 17 (b) 18 (c) 23 (d) 289
  26. 26.What is the distance between the points (0, 13) and (6, 5)? (a) 10 (b) 11 (c) 14 (d) 100
  27. 27.What is the distance between the points (6, 6) and (14, 12)? (a) 100 (b) 10 (c) 11 (d) 14
  28. 28.In which quadrant does the point (−1, 3) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  29. 29.What is the midpoint of the line joining (5, 11) and (7, 1)? (a) (7, 6) (b) (6, 6) (c) (1, 5) (d) (12, 12)
  30. 30.What is the midpoint of the line joining (2, 6) and (6, 12)? (a) (8, 18) (b) (2, 3) (c) (9, 4) (d) (4, 9)
  31. 31.What is the midpoint of the line joining (4, 3) and (16, 7)? (a) (6, 2) (b) (5, 10) (c) (10, 5) (d) (20, 10)
  32. 32.What is the midpoint of the line joining (1, 21) and (9, 9)? (a) (10, 30) (b) (5, 15) (c) (4, 6) (d) (15, 5)
  33. 33.In which quadrant does the point (7, 3) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  34. 34.What is the distance between the points (5, 16) and (14, 4)? (a) 225 (b) 15 (c) 21 (d) 16
  35. 35.What is the midpoint of the line joining (9, 11) and (21, 9)? (a) (6, 1) (b) (15, 10) (c) (10, 15) (d) (30, 20)
  36. 36.What is the distance between the points (9, 11) and (17, 5)? (a) 100 (b) 10 (c) 11 (d) 14
  37. 37.What is the distance between the points (1, 6) and (4, 2)? (a) 7 (b) 6 (c) 5 (d) 25
  38. 38.In which quadrant does the point (−6, 1) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  39. 39.What is the midpoint of the line joining (1, 7) and (9, 5)? (a) (5, 6) (b) (6, 5) (c) (4, 1) (d) (10, 12)
  40. 40.What is the distance between the points (8, 8) and (32, 15)? (a) 625 (b) 25 (c) 31 (d) 26

Answer key

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

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