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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 955 · 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.In which quadrant does the point (1, 4) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  2. 2.What is the midpoint of the line joining (1, 11) and (13, 9)? (a) (10, 7) (b) (14, 20) (c) (6, 1) (d) (7, 10)
  3. 3.What is the distance between the points (4, 20) and (20, 8)? (a) 400 (b) 21 (c) 28 (d) 20
  4. 4.How far is the point (9, 12) from the origin (0, 0)? (a) 15 (b) 21 (c) 16 (d) 225
  5. 5.In which quadrant does the point (−1, −7) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  6. 6.What is the distance between the points (9, 8) and (18, 20)? (a) 15 (b) 21 (c) 16 (d) 225
  7. 7.What is the distance between the points (6, 15) and (12, 7)? (a) 14 (b) 10 (c) 100 (d) 11
  8. 8.What is the distance between the points (2, 6) and (5, 10)? (a) 25 (b) 6 (c) 7 (d) 5
  9. 9.What is the midpoint of the line joining (10, 3) and (20, 11)? (a) (5, 4) (b) (15, 7) (c) (7, 15) (d) (30, 14)
  10. 10.What is the distance between the points (3, 25) and (10, 1)? (a) 25 (b) 26 (c) 625 (d) 31
  11. 11.What is the distance between the points (1, 24) and (9, 9)? (a) 23 (b) 289 (c) 17 (d) 18
  12. 12.What is the midpoint of the line joining (2, 2) and (14, 10)? (a) (6, 8) (b) (6, 4) (c) (8, 6) (d) (16, 12)
  13. 13.In which quadrant does the point (8, 9) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  14. 14.What is the distance between the points (4, 4) and (13, 16)? (a) 21 (b) 15 (c) 16 (d) 225
  15. 15.What is the distance between the points (2, 6) and (14, 15)? (a) 21 (b) 15 (c) 225 (d) 16
  16. 16.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 16 (c) 15 (d) 225
  17. 17.What is the distance between the points (5, 9) and (11, 1)? (a) 100 (b) 14 (c) 11 (d) 10
  18. 18.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 25 (c) 7 (d) 5
  19. 19.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 10 (c) 11 (d) 100
  20. 20.What is the distance between the points (9, 8) and (24, 16)? (a) 23 (b) 289 (c) 18 (d) 17
  21. 21.In which quadrant does the point (4, −9) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  22. 22.What is the distance between the points (3, 8) and (6, 4)? (a) 7 (b) 25 (c) 5 (d) 6
  23. 23.What is the distance between the points (9, 10) and (17, 4)? (a) 100 (b) 14 (c) 11 (d) 10
  24. 24.What is the distance between the points (0, 13) and (3, 9)? (a) 7 (b) 5 (c) 25 (d) 6
  25. 25.In which quadrant does the point (7, 1) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  26. 26.What is the midpoint of the line joining (6, 11) and (8, 5)? (a) (8, 7) (b) (1, 3) (c) (14, 16) (d) (7, 8)
  27. 27.How far is the point (5, 12) from the origin (0, 0)? (a) 13 (b) 14 (c) 169 (d) 17
  28. 28.What is the distance between the points (1, 3) and (10, 15)? (a) 16 (b) 21 (c) 225 (d) 15
  29. 29.In which quadrant does the point (−5, −5) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  30. 30.What is the distance between the points (9, 8) and (13, 5)? (a) 7 (b) 25 (c) 5 (d) 6
  31. 31.What is the midpoint of the line joining (7, 7) and (13, 11)? (a) (9, 10) (b) (3, 2) (c) (10, 9) (d) (20, 18)
  32. 32.What is the midpoint of the line joining (0, 1) and (4, 13)? (a) (2, 6) (b) (2, 7) (c) (7, 2) (d) (4, 14)
  33. 33.What is the distance between the points (6, 1) and (12, 9)? (a) 11 (b) 100 (c) 10 (d) 14
  34. 34.What is the midpoint of the line joining (5, 10) and (9, 8)? (a) (7, 9) (b) (2, 1) (c) (14, 18) (d) (9, 7)
  35. 35.In which quadrant does the point (2, 3) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  36. 36.What is the midpoint of the line joining (2, 12) and (12, 8)? (a) (14, 20) (b) (7, 10) (c) (5, 2) (d) (10, 7)
  37. 37.What is the distance between the points (1, 6) and (13, 1)? (a) 169 (b) 14 (c) 17 (d) 13
  38. 38.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 289 (c) 23 (d) 18
  39. 39.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 25 (c) 26 (d) 625
  40. 40.What is the midpoint of the line joining (7, 12) and (17, 2)? (a) (7, 12) (b) (12, 7) (c) (24, 14) (d) (5, 5)

Answer key

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

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