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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 349 · 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 (12, 16) from the origin (0, 0)? (a) 400 (b) 21 (c) 28 (d) 20
  2. 2.What is the midpoint of the line joining (9, 7) and (21, 5)? (a) (6, 15) (b) (15, 6) (c) (6, 1) (d) (30, 12)
  3. 3.What is the midpoint of the line joining (4, 6) and (14, 14)? (a) (5, 4) (b) (18, 20) (c) (9, 10) (d) (10, 9)
  4. 4.In which quadrant does the point (−9, −7) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  5. 5.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 14 (c) 100 (d) 11
  6. 6.What is the midpoint of the line joining (5, 3) and (9, 1)? (a) (2, 7) (b) (7, 2) (c) (2, 1) (d) (14, 4)
  7. 7.What is the distance between the points (8, 6) and (24, 18)? (a) 28 (b) 21 (c) 20 (d) 400
  8. 8.In which quadrant does the point (−2, −3) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  9. 9.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 17 (c) 23 (d) 289
  10. 10.In which quadrant does the point (−3, −1) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  11. 11.What is the distance between the points (2, 14) and (10, 8)? (a) 11 (b) 10 (c) 14 (d) 100
  12. 12.What is the midpoint of the line joining (6, 5) and (14, 7)? (a) (20, 12) (b) (10, 6) (c) (4, 1) (d) (6, 10)
  13. 13.What is the midpoint of the line joining (9, 0) and (11, 4)? (a) (2, 10) (b) (1, 2) (c) (20, 4) (d) (10, 2)
  14. 14.What is the distance between the points (4, 8) and (16, 17)? (a) 16 (b) 21 (c) 225 (d) 15
  15. 15.What is the midpoint of the line joining (10, 7) and (22, 15)? (a) (16, 11) (b) (32, 22) (c) (6, 4) (d) (11, 16)
  16. 16.What is the distance between the points (5, 6) and (29, 13)? (a) 625 (b) 31 (c) 25 (d) 26
  17. 17.In which quadrant does the point (−7, 8) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  18. 18.In which quadrant does the point (9, −7) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  19. 19.In which quadrant does the point (1, −2) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  20. 20.What is the distance between the points (6, 10) and (9, 6)? (a) 25 (b) 6 (c) 7 (d) 5
  21. 21.What is the distance between the points (7, 15) and (23, 3)? (a) 400 (b) 20 (c) 21 (d) 28
  22. 22.What is the distance between the points (8, 9) and (24, 21)? (a) 28 (b) 20 (c) 400 (d) 21
  23. 23.What is the distance between the points (6, 19) and (18, 3)? (a) 20 (b) 28 (c) 21 (d) 400
  24. 24.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 14 (c) 10 (d) 11
  25. 25.What is the distance between the points (0, 9) and (3, 13)? (a) 6 (b) 7 (c) 5 (d) 25
  26. 26.What is the distance between the points (7, 26) and (14, 2)? (a) 625 (b) 31 (c) 26 (d) 25
  27. 27.What is the midpoint of the line joining (7, 12) and (17, 10)? (a) (11, 12) (b) (5, 1) (c) (24, 22) (d) (12, 11)
  28. 28.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 625 (c) 25 (d) 26
  29. 29.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 400 (c) 20 (d) 28
  30. 30.What is the midpoint of the line joining (9, 18) and (11, 10)? (a) (14, 10) (b) (20, 28) (c) (1, 4) (d) (10, 14)
  31. 31.What is the distance between the points (6, 30) and (13, 6)? (a) 26 (b) 31 (c) 25 (d) 625
  32. 32.In which quadrant does the point (5, 6) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  33. 33.What is the distance between the points (2, 8) and (10, 14)? (a) 100 (b) 10 (c) 14 (d) 11
  34. 34.What is the distance between the points (9, 11) and (17, 5)? (a) 11 (b) 10 (c) 14 (d) 100
  35. 35.What is the distance between the points (3, 10) and (27, 3)? (a) 31 (b) 625 (c) 26 (d) 25
  36. 36.What is the midpoint of the line joining (8, 9) and (16, 17)? (a) (4, 4) (b) (24, 26) (c) (12, 13) (d) (13, 12)
  37. 37.What is the distance between the points (1, 16) and (25, 9)? (a) 25 (b) 31 (c) 625 (d) 26
  38. 38.What is the distance between the points (3, 17) and (15, 1)? (a) 21 (b) 400 (c) 20 (d) 28
  39. 39.How far is the point (12, 9) from the origin (0, 0)? (a) 16 (b) 15 (c) 225 (d) 21
  40. 40.What is the midpoint of the line joining (3, 2) and (5, 8)? (a) (5, 4) (b) (8, 10) (c) (1, 3) (d) (4, 5)

Answer key

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

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