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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 205 · 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 (2, 13) and (18, 1)? (a) 400 (b) 28 (c) 21 (d) 20
  2. 2.What is the midpoint of the line joining (8, 10) and (18, 18)? (a) (13, 14) (b) (26, 28) (c) (5, 4) (d) (14, 13)
  3. 3.In which quadrant does the point (7, 4) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  4. 4.In which quadrant does the point (5, −2) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  5. 5.What is the distance between the points (8, 15) and (16, 0)? (a) 17 (b) 289 (c) 23 (d) 18
  6. 6.What is the midpoint of the line joining (8, 10) and (12, 20)? (a) (10, 15) (b) (15, 10) (c) (2, 5) (d) (20, 30)
  7. 7.In which quadrant does the point (7, −7) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  8. 8.What is the midpoint of the line joining (1, 18) and (7, 6)? (a) (12, 4) (b) (8, 24) (c) (3, 6) (d) (4, 12)
  9. 9.What is the distance between the points (0, 16) and (16, 4)? (a) 21 (b) 400 (c) 20 (d) 28
  10. 10.In which quadrant does the point (6, −4) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  11. 11.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 7 (c) 5 (d) 6
  12. 12.In which quadrant does the point (−9, −4) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  13. 13.What is the distance between the points (8, 5) and (20, 21)? (a) 28 (b) 21 (c) 20 (d) 400
  14. 14.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 225 (c) 15 (d) 21
  15. 15.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 100 (c) 10 (d) 14
  16. 16.What is the distance between the points (2, 9) and (14, 4)? (a) 14 (b) 17 (c) 169 (d) 13
  17. 17.What is the midpoint of the line joining (5, 16) and (13, 10)? (a) (4, 3) (b) (9, 13) (c) (18, 26) (d) (13, 9)
  18. 18.What is the distance between the points (6, 12) and (11, 0)? (a) 17 (b) 13 (c) 169 (d) 14
  19. 19.What is the midpoint of the line joining (10, 10) and (20, 18)? (a) (15, 14) (b) (30, 28) (c) (5, 4) (d) (14, 15)
  20. 20.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 21 (c) 20 (d) 28
  21. 21.In which quadrant does the point (−1, 8) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  22. 22.What is the midpoint of the line joining (7, 13) and (13, 7)? (a) (3, 3) (b) (11, 10) (c) (20, 20) (d) (10, 10)
  23. 23.What is the distance between the points (1, 18) and (9, 3)? (a) 289 (b) 23 (c) 18 (d) 17
  24. 24.What is the midpoint of the line joining (1, 18) and (11, 10)? (a) (5, 4) (b) (14, 6) (c) (12, 28) (d) (6, 14)
  25. 25.What is the distance between the points (6, 1) and (9, 5)? (a) 7 (b) 25 (c) 5 (d) 6
  26. 26.What is the midpoint of the line joining (9, 9) and (19, 15)? (a) (14, 12) (b) (28, 24) (c) (12, 14) (d) (5, 3)
  27. 27.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 289 (c) 23 (d) 18
  28. 28.What is the midpoint of the line joining (3, 2) and (15, 6)? (a) (9, 4) (b) (4, 9) (c) (18, 8) (d) (6, 2)
  29. 29.What is the midpoint of the line joining (3, 8) and (7, 18)? (a) (5, 13) (b) (10, 26) (c) (13, 5) (d) (2, 5)
  30. 30.What is the midpoint of the line joining (3, 14) and (5, 2)? (a) (8, 16) (b) (8, 4) (c) (4, 8) (d) (1, 6)
  31. 31.In which quadrant does the point (−6, 3) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  32. 32.What is the distance between the points (3, 5) and (11, 20)? (a) 289 (b) 18 (c) 17 (d) 23
  33. 33.What is the midpoint of the line joining (3, 9) and (15, 11)? (a) (18, 20) (b) (6, 1) (c) (10, 9) (d) (9, 10)
  34. 34.In which quadrant does the point (5, −9) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  35. 35.What is the distance between the points (4, 14) and (13, 2)? (a) 21 (b) 225 (c) 16 (d) 15
  36. 36.What is the distance between the points (8, 4) and (11, 0)? (a) 25 (b) 7 (c) 6 (d) 5
  37. 37.In which quadrant does the point (9, −3) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  38. 38.What is the distance between the points (9, 18) and (17, 3)? (a) 18 (b) 23 (c) 289 (d) 17
  39. 39.What is the distance between the points (1, 15) and (25, 8)? (a) 26 (b) 31 (c) 625 (d) 25
  40. 40.What is the distance between the points (9, 9) and (21, 14)? (a) 17 (b) 13 (c) 14 (d) 169

Answer key

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

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