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Coordinate Geometry Worksheet for Maths Olympiad

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

Answer key

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

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