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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 397 · 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, 17) and (19, 5)? (a) 21 (b) 20 (c) 28 (d) 400
  2. 2.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 14 (c) 10 (d) 100
  3. 3.What is the midpoint of the line joining (8, 10) and (14, 6)? (a) (11, 8) (b) (22, 16) (c) (3, 2) (d) (8, 11)
  4. 4.What is the midpoint of the line joining (6, 6) and (8, 0)? (a) (14, 6) (b) (3, 7) (c) (1, 3) (d) (7, 3)
  5. 5.What is the midpoint of the line joining (1, 8) and (13, 18)? (a) (6, 5) (b) (14, 26) (c) (13, 7) (d) (7, 13)
  6. 6.What is the midpoint of the line joining (6, 16) and (18, 8)? (a) (12, 12) (b) (13, 12) (c) (6, 4) (d) (24, 24)
  7. 7.How far is the point (16, 12) from the origin (0, 0)? (a) 400 (b) 28 (c) 21 (d) 20
  8. 8.What is the midpoint of the line joining (0, 15) and (2, 5)? (a) (1, 10) (b) (10, 1) (c) (2, 20) (d) (1, 5)
  9. 9.What is the distance between the points (9, 2) and (18, 14)? (a) 225 (b) 21 (c) 16 (d) 15
  10. 10.In which quadrant does the point (1, 9) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  11. 11.In which quadrant does the point (−6, −9) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  12. 12.What is the distance between the points (0, 2) and (12, 11)? (a) 15 (b) 225 (c) 16 (d) 21
  13. 13.In which quadrant does the point (7, 2) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  14. 14.What is the midpoint of the line joining (1, 16) and (3, 8)? (a) (12, 2) (b) (1, 4) (c) (2, 12) (d) (4, 24)
  15. 15.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 28 (c) 20 (d) 400
  16. 16.What is the midpoint of the line joining (0, 8) and (2, 0)? (a) (2, 8) (b) (2, 4) (c) (1, 4) (d) (4, 1)
  17. 17.What is the distance between the points (9, 4) and (33, 11)? (a) 31 (b) 25 (c) 625 (d) 26
  18. 18.What is the distance between the points (0, 8) and (8, 23)? (a) 289 (b) 23 (c) 18 (d) 17
  19. 19.What is the midpoint of the line joining (3, 11) and (5, 7)? (a) (4, 9) (b) (1, 2) (c) (9, 4) (d) (8, 18)
  20. 20.In which quadrant does the point (−2, 8) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  21. 21.What is the distance between the points (7, 1) and (19, 10)? (a) 21 (b) 225 (c) 16 (d) 15
  22. 22.In which quadrant does the point (7, 8) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  23. 23.In which quadrant does the point (7, 3) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  24. 24.What is the midpoint of the line joining (0, 0) and (6, 10)? (a) (4, 5) (b) (5, 3) (c) (3, 5) (d) (6, 10)
  25. 25.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 25 (c) 625 (d) 26
  26. 26.In which quadrant does the point (−2, −4) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  27. 27.What is the distance between the points (2, 2) and (14, 11)? (a) 16 (b) 21 (c) 15 (d) 225
  28. 28.In which quadrant does the point (−5, −6) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  29. 29.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 14 (c) 10 (d) 11
  30. 30.What is the distance between the points (9, 8) and (24, 0)? (a) 289 (b) 18 (c) 17 (d) 23
  31. 31.In which quadrant does the point (4, 9) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  32. 32.What is the distance between the points (8, 16) and (13, 4)? (a) 169 (b) 14 (c) 17 (d) 13
  33. 33.What is the distance between the points (2, 21) and (11, 9)? (a) 16 (b) 21 (c) 225 (d) 15
  34. 34.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 6 (c) 5 (d) 25
  35. 35.What is the distance between the points (8, 9) and (15, 33)? (a) 625 (b) 31 (c) 25 (d) 26
  36. 36.What is the distance between the points (5, 0) and (17, 5)? (a) 14 (b) 13 (c) 17 (d) 169
  37. 37.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 15 (c) 225 (d) 16
  38. 38.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 18 (c) 17 (d) 289
  39. 39.How far is the point (5, 12) from the origin (0, 0)? (a) 13 (b) 14 (c) 17 (d) 169
  40. 40.What is the midpoint of the line joining (0, 7) and (8, 15)? (a) (4, 4) (b) (4, 11) (c) (11, 4) (d) (8, 22)

Answer key

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

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