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  4. For the given line 3x-4y=8 , the points (2, 3) and (-4, 5) are on the

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Q. For the given line $ 3x-4y=8 $ , the points $ (2,\,\,3) $ and $ (-4,\,\,5) $ are on the

Jharkhand CECEJharkhand CECE 2010

Solution:

We have, the line $ L=3x-4y-8 $ ... (i)
and the points $ (2,\,\,3) $ and $ (-4,\,\,5) $ .
Putting the points $ (2,\,\,3) $ and $ (-4,\,\,5) $ on the given line (i),
we get $ 3(2)-4(3)-8 $ $ =6-12-8<0 $ (negative) and
$ 3(-4)-4(5)-8 $ $ =-12-20-8<0 $ (negative)
By putting both the points in Eq. (i), we get that both have same sign (negative). Hence, both the points are on the same side.