Let $L$ be the line $y=2 x$, in the two dimensional plane. Statement 1: The image of the point $(0,1)$ in…
Let $L$ be the line $y=2 x$, in the two dimensional plane.
Statement 1: The image of the point $(0,1)$ in $L$ is the point $\left(\frac{4}{5}, \frac{3}{5}\right)$
Statement 2: The points $(0,1)$ and $\left(\frac{4}{5}, \frac{3}{5}\right)$ lie on opposite sides of the line $\mathrm{L}$ and are at equal distance from it.
Statement 1 is true, Statement 2 is false.
Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 1.
Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1.
Statement 1 is false, Statement 2 is true.
Solution
Statement - 1
Let $P^{\prime}\left(x_1, y_1\right)$ be the image of $(0,1)$ with respect to the line $2 x-y=0$ then
$
\begin{aligned}
& \frac{x_1}{2}=\frac{y_1-1}{-1}=\frac{-4(0)+2(1)}{5} \\
& \Rightarrow x_1=\frac{4}{5}, y_1=\frac{3}{5}
\end{aligned}
$
Thus, statement- 1 is true.
Also, statement-2 is true and correct explanation for statement-1