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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 817 · 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, 20) and (8, 5)? (a) 289 (b) 18 (c) 23 (d) 17
  2. 2.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 18 (c) 17 (d) 23
  3. 3.What is the distance between the points (7, 17) and (19, 1)? (a) 28 (b) 400 (c) 20 (d) 21
  4. 4.What is the distance between the points (5, 4) and (9, 7)? (a) 7 (b) 5 (c) 25 (d) 6
  5. 5.What is the midpoint of the line joining (0, 10) and (6, 8)? (a) (3, 9) (b) (3, 1) (c) (6, 18) (d) (9, 3)
  6. 6.In which quadrant does the point (2, −7) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  7. 7.What is the distance between the points (4, 1) and (19, 9)? (a) 289 (b) 18 (c) 23 (d) 17
  8. 8.What is the distance between the points (5, 2) and (17, 7)? (a) 169 (b) 14 (c) 17 (d) 13
  9. 9.What is the distance between the points (7, 11) and (22, 3)? (a) 289 (b) 17 (c) 18 (d) 23
  10. 10.What is the distance between the points (0, 20) and (16, 8)? (a) 28 (b) 20 (c) 400 (d) 21
  11. 11.What is the midpoint of the line joining (5, 9) and (9, 1)? (a) (14, 10) (b) (2, 4) (c) (7, 5) (d) (5, 7)
  12. 12.What is the distance between the points (4, 1) and (7, 5)? (a) 25 (b) 6 (c) 7 (d) 5
  13. 13.What is the midpoint of the line joining (10, 19) and (18, 9)? (a) (15, 14) (b) (14, 14) (c) (4, 5) (d) (28, 28)
  14. 14.How far is the point (16, 12) from the origin (0, 0)? (a) 400 (b) 28 (c) 21 (d) 20
  15. 15.In which quadrant does the point (−5, −5) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  16. 16.What is the midpoint of the line joining (1, 6) and (11, 18)? (a) (6, 12) (b) (12, 24) (c) (12, 6) (d) (5, 6)
  17. 17.In which quadrant does the point (5, 2) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  18. 18.What is the midpoint of the line joining (1, 2) and (9, 14)? (a) (5, 8) (b) (4, 6) (c) (8, 5) (d) (10, 16)
  19. 19.What is the distance between the points (4, 2) and (16, 11)? (a) 15 (b) 21 (c) 225 (d) 16
  20. 20.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 28 (c) 400 (d) 20
  21. 21.What is the distance between the points (1, 19) and (17, 7)? (a) 20 (b) 21 (c) 28 (d) 400
  22. 22.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 25 (c) 31 (d) 26
  23. 23.What is the distance between the points (9, 9) and (17, 3)? (a) 100 (b) 14 (c) 10 (d) 11
  24. 24.What is the distance between the points (5, 9) and (11, 17)? (a) 11 (b) 100 (c) 14 (d) 10
  25. 25.What is the distance between the points (2, 6) and (18, 18)? (a) 400 (b) 21 (c) 20 (d) 28
  26. 26.In which quadrant does the point (1, 9) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  27. 27.In which quadrant does the point (−1, −2) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  28. 28.What is the midpoint of the line joining (5, 1) and (9, 5)? (a) (7, 3) (b) (3, 7) (c) (2, 2) (d) (14, 6)
  29. 29.What is the distance between the points (3, 6) and (6, 2)? (a) 25 (b) 5 (c) 6 (d) 7
  30. 30.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 100 (c) 10 (d) 14
  31. 31.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 17 (c) 23 (d) 18
  32. 32.What is the distance between the points (6, 7) and (14, 22)? (a) 289 (b) 17 (c) 23 (d) 18
  33. 33.What is the distance between the points (2, 8) and (14, 24)? (a) 28 (b) 21 (c) 400 (d) 20
  34. 34.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 25 (c) 6 (d) 5
  35. 35.What is the distance between the points (1, 2) and (5, 5)? (a) 6 (b) 7 (c) 25 (d) 5
  36. 36.In which quadrant does the point (−8, −5) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  37. 37.In which quadrant does the point (−1, −4) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  38. 38.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 14 (c) 13 (d) 17
  39. 39.In which quadrant does the point (−2, −3) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  40. 40.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 17 (c) 13 (d) 14

Answer key

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

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