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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 366 · 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 (0, 18) and (12, 9)? (a) 16 (b) 15 (c) 21 (d) 225
  2. 2.What is the distance between the points (6, 12) and (14, 6)? (a) 10 (b) 14 (c) 100 (d) 11
  3. 3.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 25 (c) 31 (d) 26
  4. 4.What is the midpoint of the line joining (3, 1) and (13, 11)? (a) (5, 5) (b) (6, 8) (c) (8, 6) (d) (16, 12)
  5. 5.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 21 (c) 28 (d) 400
  6. 6.What is the distance between the points (7, 8) and (22, 16)? (a) 18 (b) 17 (c) 23 (d) 289
  7. 7.What is the midpoint of the line joining (1, 8) and (3, 20)? (a) (4, 28) (b) (14, 2) (c) (1, 6) (d) (2, 14)
  8. 8.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 25 (c) 5 (d) 6
  9. 9.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 25 (c) 6 (d) 5
  10. 10.What is the distance between the points (9, 17) and (17, 2)? (a) 289 (b) 18 (c) 17 (d) 23
  11. 11.What is the distance between the points (6, 13) and (30, 6)? (a) 26 (b) 625 (c) 31 (d) 25
  12. 12.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 289 (c) 17 (d) 23
  13. 13.What is the distance between the points (1, 9) and (16, 1)? (a) 18 (b) 289 (c) 23 (d) 17
  14. 14.What is the midpoint of the line joining (3, 7) and (7, 15)? (a) (10, 22) (b) (11, 5) (c) (5, 11) (d) (2, 4)
  15. 15.What is the distance between the points (2, 5) and (14, 21)? (a) 20 (b) 21 (c) 400 (d) 28
  16. 16.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 225 (c) 21 (d) 15
  17. 17.What is the distance between the points (8, 6) and (24, 18)? (a) 28 (b) 20 (c) 400 (d) 21
  18. 18.What is the midpoint of the line joining (2, 9) and (4, 11)? (a) (10, 3) (b) (3, 10) (c) (1, 1) (d) (6, 20)
  19. 19.What is the distance between the points (6, 5) and (9, 9)? (a) 25 (b) 5 (c) 6 (d) 7
  20. 20.What is the distance between the points (0, 14) and (12, 5)? (a) 16 (b) 15 (c) 21 (d) 225
  21. 21.What is the midpoint of the line joining (10, 16) and (22, 6)? (a) (11, 16) (b) (16, 11) (c) (32, 22) (d) (6, 5)
  22. 22.What is the distance between the points (1, 26) and (8, 2)? (a) 25 (b) 625 (c) 26 (d) 31
  23. 23.What is the distance between the points (2, 0) and (14, 9)? (a) 21 (b) 225 (c) 15 (d) 16
  24. 24.What is the midpoint of the line joining (8, 9) and (14, 19)? (a) (11, 14) (b) (14, 11) (c) (22, 28) (d) (3, 5)
  25. 25.What is the distance between the points (0, 7) and (9, 19)? (a) 225 (b) 21 (c) 15 (d) 16
  26. 26.What is the distance between the points (8, 5) and (16, 11)? (a) 100 (b) 14 (c) 11 (d) 10
  27. 27.What is the distance between the points (9, 7) and (16, 31)? (a) 25 (b) 26 (c) 31 (d) 625
  28. 28.What is the midpoint of the line joining (8, 1) and (20, 7)? (a) (6, 3) (b) (28, 8) (c) (14, 4) (d) (4, 14)
  29. 29.In which quadrant does the point (5, 2) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  30. 30.What is the distance between the points (4, 4) and (7, 8)? (a) 6 (b) 5 (c) 25 (d) 7
  31. 31.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 11 (c) 100 (d) 14
  32. 32.In which quadrant does the point (2, −6) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  33. 33.What is the distance between the points (0, 14) and (16, 2)? (a) 20 (b) 21 (c) 28 (d) 400
  34. 34.What is the distance between the points (2, 13) and (18, 1)? (a) 28 (b) 400 (c) 21 (d) 20
  35. 35.What is the distance between the points (6, 5) and (14, 11)? (a) 10 (b) 11 (c) 14 (d) 100
  36. 36.What is the distance between the points (1, 5) and (17, 17)? (a) 21 (b) 400 (c) 20 (d) 28
  37. 37.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 18 (c) 289 (d) 17
  38. 38.In which quadrant does the point (4, −4) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  39. 39.What is the distance between the points (4, 12) and (19, 4)? (a) 23 (b) 289 (c) 17 (d) 18
  40. 40.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 15 (c) 16 (d) 21

Answer key

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

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