Question

Solve Q no 18 c
Ans.=x+y+1=0
Its neccessary for my exam.

Answer 1

The points A = (3,-4)...   A'=(-7,-4),  A'' =(-7, 6)

AA'' = y + x + 1 = 0

     A simple way is the graph.

    This is quick if the mirrors are parallel or perpendicular to x or y axis.  Mirror forms the image is at the same perpendicular distance behind it, as the point is in front of it.  So we need to find the perpendicular distances.

After we have found  A'' as (-7, 6), the equation is found as:
      (y - 6)/(x+7) = (6 - (-4)) /(-7 - 3) = 10/-10 =  -1
       y - 6 + x + 7 = 0
       y + x + 1 = 0.

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In general for any type of mirror inclined or not.... 

 Equation of the Mirroring Line be :   a x + b y + c = 0
 Given Point P be (x₁, y₁).    
 Its mirror image is  P' (x₁', y₁')   where,

        (x₁' - x₁) / a  =   (y₁' - y₁) / b    =  - 2 (a x₁ + b y₁ + c)/ (a² + b²)

$\frac{x'_1 - x_1}{a} = \frac{y'_1-y_1}{b} = \frac{-2 \: (a \: x_1+b \: y_1 + c)}{a^2+b^2}\\\\x'_1=x_1-\frac{2a(a \: x_1+b \: y_1 + c)}{a^2+b^2}\\\\y'_1=y_1-\frac{2b(a \: x_1+b \: y_1 + c)}{a^2+b^2}$

   We use this formula twice in order to get the answer of the given problem.