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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 390 · 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 (2, 6) and (10, 0)? (a) 11 (b) 100 (c) 10 (d) 14
  2. 2.What is the midpoint of the line joining (1, 4) and (5, 2)? (a) (4, 3) (b) (2, 1) (c) (6, 6) (d) (3, 3)
  3. 3.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 11 (c) 14 (d) 10
  4. 4.What is the midpoint of the line joining (6, 6) and (18, 10)? (a) (6, 2) (b) (12, 8) (c) (8, 12) (d) (24, 16)
  5. 5.How far is the point (24, 7) from the origin (0, 0)? (a) 25 (b) 625 (c) 26 (d) 31
  6. 6.What is the distance between the points (3, 7) and (11, 22)? (a) 289 (b) 18 (c) 23 (d) 17
  7. 7.In which quadrant does the point (2, −1) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  8. 8.What is the midpoint of the line joining (5, 17) and (7, 5)? (a) (1, 6) (b) (12, 22) (c) (11, 6) (d) (6, 11)
  9. 9.In which quadrant does the point (−4, 1) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  10. 10.What is the midpoint of the line joining (9, 1) and (11, 3)? (a) (2, 10) (b) (10, 2) (c) (1, 1) (d) (20, 4)
  11. 11.What is the midpoint of the line joining (6, 18) and (18, 6)? (a) (6, 6) (b) (12, 12) (c) (24, 24) (d) (13, 12)
  12. 12.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 7 (c) 6 (d) 5
  13. 13.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 18 (c) 23 (d) 17
  14. 14.In which quadrant does the point (9, −2) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  15. 15.What is the distance between the points (7, 15) and (31, 8)? (a) 625 (b) 25 (c) 31 (d) 26
  16. 16.In which quadrant does the point (−2, 1) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  17. 17.What is the midpoint of the line joining (8, 10) and (14, 20)? (a) (22, 30) (b) (11, 15) (c) (15, 11) (d) (3, 5)
  18. 18.What is the distance between the points (2, 16) and (26, 9)? (a) 625 (b) 26 (c) 31 (d) 25
  19. 19.What is the distance between the points (0, 8) and (12, 17)? (a) 21 (b) 15 (c) 225 (d) 16
  20. 20.What is the midpoint of the line joining (6, 4) and (18, 12)? (a) (6, 4) (b) (24, 16) (c) (12, 8) (d) (8, 12)
  21. 21.What is the distance between the points (1, 9) and (13, 4)? (a) 13 (b) 14 (c) 17 (d) 169
  22. 22.What is the midpoint of the line joining (2, 3) and (6, 7)? (a) (5, 4) (b) (8, 10) (c) (2, 2) (d) (4, 5)
  23. 23.What is the distance between the points (1, 9) and (5, 12)? (a) 6 (b) 5 (c) 7 (d) 25
  24. 24.What is the distance between the points (3, 11) and (7, 8)? (a) 5 (b) 7 (c) 6 (d) 25
  25. 25.What is the distance between the points (0, 5) and (12, 0)? (a) 14 (b) 17 (c) 169 (d) 13
  26. 26.What is the distance between the points (2, 2) and (26, 9)? (a) 26 (b) 25 (c) 31 (d) 625
  27. 27.In which quadrant does the point (−6, 1) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  28. 28.In which quadrant does the point (9, −1) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  29. 29.In which quadrant does the point (−6, −2) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  30. 30.In which quadrant does the point (5, 7) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  31. 31.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 20 (c) 400 (d) 28
  32. 32.In which quadrant does the point (4, 8) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  33. 33.What is the distance between the points (9, 10) and (12, 6)? (a) 25 (b) 6 (c) 5 (d) 7
  34. 34.In which quadrant does the point (4, 3) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  35. 35.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 169 (c) 13 (d) 14
  36. 36.What is the midpoint of the line joining (1, 4) and (7, 6)? (a) (3, 1) (b) (8, 10) (c) (4, 5) (d) (5, 4)
  37. 37.What is the midpoint of the line joining (2, 7) and (8, 9)? (a) (10, 16) (b) (5, 8) (c) (3, 1) (d) (8, 5)
  38. 38.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 11 (c) 10 (d) 100
  39. 39.What is the distance between the points (5, 0) and (17, 9)? (a) 21 (b) 15 (c) 16 (d) 225
  40. 40.What is the distance between the points (3, 12) and (18, 4)? (a) 23 (b) 17 (c) 289 (d) 18

Answer key

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

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