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3 and 5 are intercepts of a line L=0 , then the distance of L=0 from (3,7) is

Options

  1. A21 34
  2. B34 31
  3. C34
  4. D31

Correct answer

A. 21 34

Step-by-step solution

The intercept form of a line with x-intercept a and y-intercept b is given by x a + y b = 1 . Given a = 3 and b = 5 , the equation of the line L=0 is x 3 + y 5 = 1 . Multiplying by 15, we get 5x + 3y = 15 , or 5x + 3y - 15 = 0 . The distance d of a point (x₁, y₁) from the line Ax + By + C = 0 is given by d = |Ax₁ + By₁ + C| A^2 + B^2 . Substituting (x₁, y₁) = (3, 7) , A = 5 , B = 3 , and C = -15 : d = |5(3) + 3(7) - 15| 5^2 + 3^2 d = |15 + 21 - 15| 25 + 9 d = 21 34 Answer: 21 34

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