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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 147 · 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, 2) and (14, 17)? (a) 289 (b) 18 (c) 17 (d) 23
  2. 2.What is the distance between the points (2, 17) and (14, 1)? (a) 400 (b) 20 (c) 28 (d) 21
  3. 3.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 11 (c) 10 (d) 100
  4. 4.What is the distance between the points (2, 14) and (14, 5)? (a) 15 (b) 21 (c) 16 (d) 225
  5. 5.What is the distance between the points (0, 17) and (9, 5)? (a) 225 (b) 15 (c) 16 (d) 21
  6. 6.In which quadrant does the point (1, −2) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  7. 7.What is the distance between the points (9, 4) and (12, 0)? (a) 5 (b) 25 (c) 7 (d) 6
  8. 8.What is the midpoint of the line joining (9, 11) and (19, 9)? (a) (5, 1) (b) (28, 20) (c) (14, 10) (d) (10, 14)
  9. 9.What is the distance between the points (9, 9) and (25, 21)? (a) 21 (b) 20 (c) 28 (d) 400
  10. 10.In which quadrant does the point (−3, −7) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  11. 11.What is the midpoint of the line joining (3, 3) and (11, 9)? (a) (6, 7) (b) (4, 3) (c) (7, 6) (d) (14, 12)
  12. 12.What is the distance between the points (1, 0) and (8, 24)? (a) 31 (b) 26 (c) 25 (d) 625
  13. 13.What is the midpoint of the line joining (2, 4) and (6, 2)? (a) (3, 4) (b) (4, 3) (c) (8, 6) (d) (2, 1)
  14. 14.In which quadrant does the point (7, 8) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  15. 15.What is the midpoint of the line joining (4, 6) and (10, 4)? (a) (7, 5) (b) (3, 1) (c) (14, 10) (d) (5, 7)
  16. 16.In which quadrant does the point (9, 1) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  17. 17.What is the midpoint of the line joining (0, 6) and (8, 0)? (a) (5, 3) (b) (3, 4) (c) (8, 6) (d) (4, 3)
  18. 18.What is the distance between the points (1, 4) and (17, 16)? (a) 28 (b) 400 (c) 21 (d) 20
  19. 19.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 225 (c) 15 (d) 16
  20. 20.What is the midpoint of the line joining (1, 9) and (3, 21)? (a) (15, 2) (b) (1, 6) (c) (4, 30) (d) (2, 15)
  21. 21.In which quadrant does the point (−8, 8) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  22. 22.How far is the point (7, 24) from the origin (0, 0)? (a) 25 (b) 26 (c) 625 (d) 31
  23. 23.What is the distance between the points (2, 2) and (5, 6)? (a) 25 (b) 5 (c) 6 (d) 7
  24. 24.What is the distance between the points (9, 14) and (15, 6)? (a) 11 (b) 100 (c) 10 (d) 14
  25. 25.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 25 (c) 6 (d) 5
  26. 26.What is the midpoint of the line joining (8, 9) and (20, 11)? (a) (6, 1) (b) (28, 20) (c) (10, 14) (d) (14, 10)
  27. 27.What is the distance between the points (2, 2) and (9, 26)? (a) 31 (b) 25 (c) 26 (d) 625
  28. 28.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 18 (c) 17 (d) 289
  29. 29.What is the midpoint of the line joining (9, 5) and (19, 7)? (a) (5, 1) (b) (28, 12) (c) (6, 14) (d) (14, 6)
  30. 30.In which quadrant does the point (−2, −6) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  31. 31.What is the midpoint of the line joining (0, 9) and (2, 3)? (a) (1, 6) (b) (2, 12) (c) (1, 3) (d) (6, 1)
  32. 32.In which quadrant does the point (5, 1) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  33. 33.In which quadrant does the point (1, −1) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  34. 34.How far is the point (12, 16) from the origin (0, 0)? (a) 20 (b) 400 (c) 21 (d) 28
  35. 35.What is the midpoint of the line joining (0, 12) and (2, 10)? (a) (11, 1) (b) (2, 22) (c) (1, 11) (d) (1, 1)
  36. 36.What is the midpoint of the line joining (8, 21) and (10, 9)? (a) (1, 6) (b) (18, 30) (c) (15, 9) (d) (9, 15)
  37. 37.In which quadrant does the point (9, −2) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  38. 38.What is the distance between the points (2, 14) and (26, 7)? (a) 26 (b) 31 (c) 625 (d) 25
  39. 39.What is the distance between the points (0, 2) and (4, 5)? (a) 25 (b) 6 (c) 5 (d) 7
  40. 40.What is the distance between the points (7, 5) and (19, 0)? (a) 17 (b) 13 (c) 14 (d) 169

Answer key

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

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