Q67 / 200 · TS EAMCET 2002 · Mathematics
If $(-2, 6)$ is the image of the point $(4, 2)$ with respect to the line $L = 0$, then $L$ is equal to
- A$6x - 4y - 7 = 0$
- B$2x + 3y - 5 = 0$
- Correct answerC$3x - 2y + 5 = 0$
- D$3x - 2y + 10 = 0$
Solution
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, $$ \begin{aligned} y-4 & =\frac{3}{2}(x-1) \\ \Rightarrow \quad 2 y-8 & =3 x-3 \\ \Rightarrow \quad 3 x-2 y+5 & =0 \end{aligned} $$
Hence, the correct answer is option: 'C'.