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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 429 · 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 midpoint of the line joining (0, 15) and (6, 3)? (a) (3, 6) (b) (3, 9) (c) (9, 3) (d) (6, 18)
  2. 2.What is the distance between the points (0, 18) and (16, 6)? (a) 28 (b) 20 (c) 400 (d) 21
  3. 3.What is the distance between the points (0, 15) and (12, 6)? (a) 21 (b) 15 (c) 16 (d) 225
  4. 4.In which quadrant does the point (−3, −6) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  5. 5.What is the midpoint of the line joining (1, 6) and (3, 16)? (a) (1, 5) (b) (2, 11) (c) (11, 2) (d) (4, 22)
  6. 6.In which quadrant does the point (−6, 3) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  7. 7.In which quadrant does the point (9, 5) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  8. 8.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 25 (c) 7 (d) 5
  9. 9.What is the distance between the points (5, 0) and (10, 12)? (a) 169 (b) 13 (c) 14 (d) 17
  10. 10.What is the midpoint of the line joining (10, 6) and (22, 12)? (a) (32, 18) (b) (16, 9) (c) (9, 16) (d) (6, 3)
  11. 11.In which quadrant does the point (6, −3) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  12. 12.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 289 (c) 17 (d) 18
  13. 13.What is the distance between the points (7, 5) and (31, 12)? (a) 625 (b) 31 (c) 26 (d) 25
  14. 14.What is the distance between the points (9, 12) and (14, 0)? (a) 14 (b) 169 (c) 13 (d) 17
  15. 15.What is the midpoint of the line joining (3, 18) and (11, 8)? (a) (4, 5) (b) (13, 7) (c) (7, 13) (d) (14, 26)
  16. 16.What is the midpoint of the line joining (1, 10) and (11, 0)? (a) (5, 6) (b) (12, 10) (c) (5, 5) (d) (6, 5)
  17. 17.What is the distance between the points (6, 2) and (12, 10)? (a) 14 (b) 10 (c) 11 (d) 100
  18. 18.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 18 (c) 289 (d) 23
  19. 19.What is the midpoint of the line joining (1, 6) and (5, 8)? (a) (2, 1) (b) (3, 7) (c) (7, 3) (d) (6, 14)
  20. 20.In which quadrant does the point (2, −2) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  21. 21.In which quadrant does the point (3, −1) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  22. 22.In which quadrant does the point (−2, 1) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  23. 23.What is the distance between the points (9, 5) and (21, 0)? (a) 14 (b) 17 (c) 169 (d) 13
  24. 24.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 100 (c) 14 (d) 11
  25. 25.In which quadrant does the point (−3, 7) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  26. 26.What is the distance between the points (3, 11) and (9, 3)? (a) 11 (b) 100 (c) 14 (d) 10
  27. 27.What is the distance between the points (8, 24) and (15, 0)? (a) 625 (b) 25 (c) 31 (d) 26
  28. 28.What is the distance between the points (8, 9) and (20, 18)? (a) 21 (b) 16 (c) 225 (d) 15
  29. 29.In which quadrant does the point (6, 1) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  30. 30.What is the distance between the points (0, 9) and (8, 15)? (a) 10 (b) 100 (c) 14 (d) 11
  31. 31.What is the midpoint of the line joining (2, 13) and (4, 5)? (a) (6, 18) (b) (1, 4) (c) (3, 9) (d) (9, 3)
  32. 32.What is the distance between the points (2, 14) and (26, 7)? (a) 26 (b) 31 (c) 625 (d) 25
  33. 33.In which quadrant does the point (−8, −2) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  34. 34.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 100 (c) 14 (d) 10
  35. 35.In which quadrant does the point (9, −8) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  36. 36.In which quadrant does the point (−8, −3) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  37. 37.What is the midpoint of the line joining (9, 0) and (21, 4)? (a) (6, 2) (b) (2, 15) (c) (15, 2) (d) (30, 4)
  38. 38.What is the midpoint of the line joining (7, 0) and (17, 6)? (a) (3, 12) (b) (24, 6) (c) (12, 3) (d) (5, 3)
  39. 39.What is the distance between the points (5, 14) and (29, 7)? (a) 31 (b) 25 (c) 625 (d) 26
  40. 40.What is the distance between the points (5, 0) and (13, 6)? (a) 10 (b) 14 (c) 11 (d) 100

Answer key

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

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