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If the equation of the hypotenuse of a right-angled isosceles triangle is 3 x + 4 y = 4 and its opposite vertex is 2,2 , then the equations of the perpendicular and the base are respectively

Options

  1. A7 x + y = 16   &   x - 7 y + 12 = 0
  2. B7 x - y = 12 & x + 7 y = 16
  3. C5 x + y = 12 & x - 5 y + 8 = 0
  4. Dx + 5 y = 12 & 5 x - y = 8

Correct answer

A. 7 x + y = 16   &   x - 7 y + 12 = 0

Step-by-step solution

Let, the slope of the required line is m , then m - - 3 4 1 + m - 3 4 = ± tan ⁡ 45 o 4 m + 3 = ± 4 - 3 m ⇒ m = - 7 , 1 7 ⇒ equation of the lines are y - 2 x - 2 = - 7 & y - 2 x - 2 = 1 7 ⇒ 7 x + y = 16   &     x - 7 y + 12 = 0

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