Explanation

(a)
Here, $\left( x_{1},\ y_{1} \right) = (3,\ 4)\ and\ ax + by + c = 2x + y - 7 = 0$
$\therefore a = 2,\ \ b = 1,\ \ c = - 7$
Let, $(h,k)$ be the coordinates of the foot.
Then,
$\frac{h - 3}{2} = \frac{k - 4}{1} = \frac{- (2 \times 3 + 1 \times 4 - 7)}{2^{2} + 1^{2}} = \frac{- 3}{5}$
$\Rightarrow \frac{h - 3}{2} = \frac{- 3}{5}\ and\frac{k - 4}{1} = \frac{- 3}{5}$
$\Rightarrow h = \frac{- 6}{5} + 3\ and\ k = \frac{- 3}{5} + 4$
$\Rightarrow h = \frac{9}{5}\ and\ k = \frac{17}{5}$
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