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  4. The image of the origin with reference to the line 4x+3y-25=0 is:

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Q. The image of the origin with reference to the line $ 4x+3y-25=0 $ is:

KEAMKEAM 2005

Solution:

Let the image or (reflection) of the origin with reference to the line
$ 4x+3y-25=0 $ is $ (h,k) $
$ \therefore $ $ \frac{h-0}{4}=\frac{k-0}{3} $
$ =\frac{-2(0+0-25)}{16+9}=\frac{50}{25}=2 $
$ \Rightarrow $ $ \frac{h}{4}=2\Rightarrow h=8 $
and $ \frac{k}{3}=2\Rightarrow k=6 $
$ \therefore $ Required point is (8, 6).