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If $(h, k)$ is the image of the point $(2,-3)$ with respect to the line $5 x-3 y=2$, then $h+k$ is equal to
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1139 Upvotes
Verified Answer
The correct answer is:
-3
By formula,
$$
\frac{h-2}{5}=\frac{k+3}{-3}=\frac{-2(5 \times 2-3 \times(-3)-2)}{(5)^2+(-3)^2}
$$
$\begin{array}{llrl}\Rightarrow & \frac{h-2}{5} =\frac{k+3}{-3}=-1 \\ \Rightarrow & h-2 =-5 \text { and } k+3=3 \\ \Rightarrow & h =-3 \text { and } k=0 \\ \therefore & h+k =-3+0=-3\end{array}$
$$
\frac{h-2}{5}=\frac{k+3}{-3}=\frac{-2(5 \times 2-3 \times(-3)-2)}{(5)^2+(-3)^2}
$$
$\begin{array}{llrl}\Rightarrow & \frac{h-2}{5} =\frac{k+3}{-3}=-1 \\ \Rightarrow & h-2 =-5 \text { and } k+3=3 \\ \Rightarrow & h =-3 \text { and } k=0 \\ \therefore & h+k =-3+0=-3\end{array}$
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