Question

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.

• A. Statement 1 is true, Statement 2 is false
• B. Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 1
• C. Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1
• D. Statement 1 is false, Statement 2 is true

Answer 1

Answer: (C)

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.