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  4. Let L be the line y = 2x, in the two dimensional plane. Statement 1: The image of the point (0,1) in L is the point ((4/5), (3/5)). Statement 2: The points (0,1) and ((4/5), (3/5)) lies on opposite sides of the line L and are at equal distance from it.

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Q. Let $L$ be the line $y = 2x$, 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 $\left(\frac{4}{5}, \frac{3}{5}\right)$ lies on opposite sides of the line L and are at equal distance from it.

AIEEEAIEEE 2012Straight Lines

Solution:

Statement - 1
Let $P (x_1, y_1)$ be the image of $(0, 1)$ with respect to the line $2x - y = 0$ then
$\frac{x_{1}}{2}=\frac{y_{1}-1}{-1}=\frac{-4\left(0\right)+2\left(1\right)}{5}$
$\Rightarrow x_{1}=\frac{4}{5}, y_{1}=\frac{3}{5}$
Thus, statement-1 is true.
Also, statement-2 is true and correct explanation for statement-1.