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The distance of the point (3,4) from the line 3 x+2 y+7=0 measured along the line parallel to y-2 x+7=0 is equal to

Options

  1. A23 5 7
  2. B4 5
  3. C3 5
  4. D24 5 7

Correct answer

D. 24 5 7

Step-by-step solution

The given point is P(3, 4) and the line is L: 3x + 2y + 7 = 0 . The line along which the distance is measured is parallel to y - 2x + 7 = 0 , which has a slope m = 2 . The equation of the line passing through (3, 4) with slope m = 2 is given by y - 4 = 2(x - 3) , which simplifies to y = 2x - 2 or 2x - y - 2 = 0 . To find the intersection point Q of the line 3x + 2y + 7 = 0 and 2x - y - 2 = 0 , we solve the system: 3x + 2y = -7 4x - 2y = 4 Adding the two equations gives 7x = -3 , so x = -3/7 . Substituting x into 2x

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