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If $(-2, 6)$ is the image of the point $(4, 2)$ with respect to the line $L = 0$, then $L$ is equal to
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Verified Answer
The correct answer is:
$3x - 2y + 5 = 0$
Slope of the line $C D$
$$
=\frac{6-2}{-2-4}=\frac{4}{-6}=-\frac{2}{3}
$$
Slope of the line $A B=-\frac{1}{-\frac{2}{3}}=\frac{3}{2}$
Mid-point of $C D$ is $O\left(\frac{4-2}{2}, \frac{2+6}{2}\right)$
$$
=O(1,4)
$$
Equation of line $A B$ is,
$$
\begin{aligned}
y-4 & =\frac{3}{2}(x-1) \\
\Rightarrow \quad 2 y-8 & =3 x-3 \\
\Rightarrow \quad 3 x-2 y+5 & =0
\end{aligned}
$$
$$
=\frac{6-2}{-2-4}=\frac{4}{-6}=-\frac{2}{3}
$$
Slope of the line $A B=-\frac{1}{-\frac{2}{3}}=\frac{3}{2}$
Mid-point of $C D$ is $O\left(\frac{4-2}{2}, \frac{2+6}{2}\right)$
$$
=O(1,4)
$$
Equation of line $A B$ is,
$$
\begin{aligned}
y-4 & =\frac{3}{2}(x-1) \\
\Rightarrow \quad 2 y-8 & =3 x-3 \\
\Rightarrow \quad 3 x-2 y+5 & =0
\end{aligned}
$$
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