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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 533 · 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 distance between the points (5, 3) and (29, 10)? (a) 31 (b) 26 (c) 625 (d) 25
  3. 3.What is the distance between the points (0, 5) and (4, 8)? (a) 25 (b) 5 (c) 7 (d) 6
  4. 4.In which quadrant does the point (−4, 5) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  5. 5.What is the distance between the points (0, 22) and (12, 6)? (a) 400 (b) 21 (c) 20 (d) 28
  6. 6.What is the midpoint of the line joining (0, 7) and (8, 1)? (a) (4, 4) (b) (8, 8) (c) (5, 4) (d) (4, 3)
  7. 7.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 25 (c) 7 (d) 5
  8. 8.What is the distance between the points (1, 3) and (13, 12)? (a) 225 (b) 15 (c) 21 (d) 16
  9. 9.What is the distance between the points (6, 11) and (12, 3)? (a) 100 (b) 14 (c) 10 (d) 11
  10. 10.What is the distance between the points (6, 8) and (12, 0)? (a) 100 (b) 10 (c) 11 (d) 14
  11. 11.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 14 (c) 100 (d) 10
  12. 12.What is the midpoint of the line joining (2, 21) and (4, 9)? (a) (15, 3) (b) (1, 6) (c) (3, 15) (d) (6, 30)
  13. 13.In which quadrant does the point (−1, 5) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  14. 14.What is the midpoint of the line joining (5, 12) and (13, 0)? (a) (4, 6) (b) (6, 9) (c) (18, 12) (d) (9, 6)
  15. 15.What is the distance between the points (5, 9) and (17, 25)? (a) 400 (b) 21 (c) 28 (d) 20
  16. 16.What is the distance between the points (4, 7) and (28, 14)? (a) 625 (b) 31 (c) 26 (d) 25
  17. 17.What is the midpoint of the line joining (4, 6) and (16, 2)? (a) (20, 8) (b) (6, 2) (c) (10, 4) (d) (4, 10)
  18. 18.In which quadrant does the point (−1, 6) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  19. 19.What is the distance between the points (3, 12) and (15, 7)? (a) 169 (b) 14 (c) 17 (d) 13
  20. 20.What is the distance between the points (7, 8) and (16, 20)? (a) 225 (b) 15 (c) 16 (d) 21
  21. 21.What is the distance between the points (7, 5) and (10, 1)? (a) 25 (b) 5 (c) 7 (d) 6
  22. 22.In which quadrant does the point (5, 3) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  23. 23.What is the midpoint of the line joining (4, 19) and (12, 9)? (a) (8, 14) (b) (14, 8) (c) (16, 28) (d) (4, 5)
  24. 24.What is the distance between the points (2, 13) and (11, 1)? (a) 16 (b) 21 (c) 225 (d) 15
  25. 25.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 5 (c) 6 (d) 7
  26. 26.What is the distance between the points (2, 21) and (18, 9)? (a) 20 (b) 28 (c) 400 (d) 21
  27. 27.What is the distance between the points (7, 6) and (10, 10)? (a) 6 (b) 5 (c) 7 (d) 25
  28. 28.What is the distance between the points (0, 9) and (15, 1)? (a) 289 (b) 23 (c) 18 (d) 17
  29. 29.What is the distance between the points (4, 18) and (16, 2)? (a) 400 (b) 20 (c) 28 (d) 21
  30. 30.What is the midpoint of the line joining (2, 8) and (6, 4)? (a) (6, 4) (b) (2, 2) (c) (8, 12) (d) (4, 6)
  31. 31.What is the distance between the points (2, 0) and (10, 6)? (a) 100 (b) 11 (c) 14 (d) 10
  32. 32.What is the midpoint of the line joining (3, 0) and (9, 2)? (a) (1, 6) (b) (6, 1) (c) (12, 2) (d) (3, 1)
  33. 33.What is the midpoint of the line joining (2, 18) and (4, 10)? (a) (1, 4) (b) (3, 14) (c) (6, 28) (d) (14, 3)
  34. 34.What is the midpoint of the line joining (4, 5) and (16, 3)? (a) (10, 4) (b) (6, 1) (c) (20, 8) (d) (4, 10)
  35. 35.What is the distance between the points (4, 3) and (10, 11)? (a) 100 (b) 11 (c) 14 (d) 10
  36. 36.What is the distance between the points (2, 13) and (18, 1)? (a) 28 (b) 20 (c) 21 (d) 400
  37. 37.What is the distance between the points (2, 9) and (26, 2)? (a) 625 (b) 31 (c) 25 (d) 26
  38. 38.In which quadrant does the point (3, −3) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  39. 39.What is the distance between the points (9, 18) and (21, 2)? (a) 21 (b) 400 (c) 28 (d) 20
  40. 40.What is the distance between the points (0, 7) and (5, 19)? (a) 17 (b) 169 (c) 13 (d) 14

Answer key

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

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