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The coordinates of the points on the line 3 x + 2 y = 5 which are equidistant from the lines 4 x + 3 y - 7 = 0 and 2 y - 5 = 0 can be

Options

  1. A- 1 14 , 73 28
  2. B1 14 , - 73 28
  3. C1 16 , - 77 32
  4. D- 1 16 , 77 32

Correct answer

A. - 1 14 , 73 28

Step-by-step solution

We know that the bisectors of the angles between two lines contain all those points which are equidistant from the lines. So, the required point lies on the bisectors of the angles between the given lines. The equations of the bisectors are given by 4 x + 3 y - 7 4 2 + 3 2 = ± 2 y - 5 0 2 + 2 2 ⇒ 4 x + 3 y - 7 5 = ± 2 y - 5 2 ⇒ 8 x - 4 y + 11 = 0 and 8 x + 16 y - 39 = 0 Let, h , k be the coordinates of the required point. Then, 8 h - 4 k + 11 = 0 …(i) or, 8 h + 16 k - 39 = 0 …(ii

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