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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 386 · 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 (6, 11) and (9, 7)? (a) 25 (b) 7 (c) 6 (d) 5
  2. 2.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 23 (c) 18 (d) 289
  3. 3.What is the midpoint of the line joining (5, 21) and (7, 9)? (a) (6, 15) (b) (12, 30) (c) (15, 6) (d) (1, 6)
  4. 4.What is the distance between the points (1, 1) and (4, 5)? (a) 5 (b) 6 (c) 7 (d) 25
  5. 5.What is the distance between the points (6, 24) and (14, 9)? (a) 17 (b) 18 (c) 23 (d) 289
  6. 6.In which quadrant does the point (−1, −1) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  7. 7.In which quadrant does the point (−5, 5) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  8. 8.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 13 (c) 169 (d) 17
  9. 9.What is the midpoint of the line joining (7, 10) and (15, 8)? (a) (4, 1) (b) (9, 11) (c) (11, 9) (d) (22, 18)
  10. 10.What is the distance between the points (9, 7) and (17, 22)? (a) 289 (b) 23 (c) 17 (d) 18
  11. 11.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 400 (c) 20 (d) 21
  12. 12.What is the midpoint of the line joining (1, 18) and (5, 6)? (a) (3, 12) (b) (2, 6) (c) (12, 3) (d) (6, 24)
  13. 13.What is the midpoint of the line joining (6, 5) and (16, 7)? (a) (6, 11) (b) (22, 12) (c) (5, 1) (d) (11, 6)
  14. 14.In which quadrant does the point (9, −1) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  15. 15.What is the midpoint of the line joining (8, 5) and (12, 13)? (a) (2, 4) (b) (10, 9) (c) (9, 10) (d) (20, 18)
  16. 16.What is the distance between the points (2, 1) and (14, 6)? (a) 17 (b) 14 (c) 13 (d) 169
  17. 17.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 15 (c) 16 (d) 21
  18. 18.What is the distance between the points (0, 6) and (24, 13)? (a) 25 (b) 625 (c) 26 (d) 31
  19. 19.What is the distance between the points (4, 1) and (10, 9)? (a) 14 (b) 10 (c) 100 (d) 11
  20. 20.What is the midpoint of the line joining (3, 7) and (5, 3)? (a) (4, 5) (b) (5, 4) (c) (8, 10) (d) (1, 2)
  21. 21.What is the distance between the points (5, 20) and (17, 4)? (a) 28 (b) 400 (c) 21 (d) 20
  22. 22.In which quadrant does the point (4, 3) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  23. 23.What is the distance between the points (4, 14) and (12, 8)? (a) 14 (b) 11 (c) 100 (d) 10
  24. 24.What is the midpoint of the line joining (6, 7) and (12, 13)? (a) (9, 10) (b) (18, 20) (c) (10, 9) (d) (3, 3)
  25. 25.What is the distance between the points (4, 1) and (7, 5)? (a) 7 (b) 5 (c) 25 (d) 6
  26. 26.How far is the point (9, 12) from the origin (0, 0)? (a) 15 (b) 21 (c) 225 (d) 16
  27. 27.In which quadrant does the point (−3, −3) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  28. 28.What is the distance between the points (4, 8) and (28, 1)? (a) 31 (b) 26 (c) 625 (d) 25
  29. 29.In which quadrant does the point (2, −6) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  30. 30.What is the distance between the points (2, 5) and (17, 13)? (a) 23 (b) 17 (c) 289 (d) 18
  31. 31.In which quadrant does the point (−2, −1) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  32. 32.What is the midpoint of the line joining (1, 18) and (9, 6)? (a) (4, 6) (b) (12, 5) (c) (5, 12) (d) (10, 24)
  33. 33.What is the distance between the points (1, 18) and (10, 6)? (a) 16 (b) 225 (c) 21 (d) 15
  34. 34.What is the distance between the points (9, 9) and (21, 4)? (a) 17 (b) 14 (c) 13 (d) 169
  35. 35.What is the distance between the points (2, 8) and (14, 17)? (a) 21 (b) 225 (c) 16 (d) 15
  36. 36.In which quadrant does the point (−9, 1) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  37. 37.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 26 (c) 25 (d) 31
  38. 38.What is the distance between the points (8, 9) and (17, 21)? (a) 15 (b) 225 (c) 21 (d) 16
  39. 39.What is the distance between the points (1, 9) and (25, 16)? (a) 25 (b) 26 (c) 625 (d) 31
  40. 40.What is the midpoint of the line joining (0, 2) and (2, 4)? (a) (3, 1) (b) (1, 1) (c) (1, 3) (d) (2, 6)

Answer key

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

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