Let L be the line y = 2x in two dimensions.St | vedclass

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(A) The line $L$ is given by $2x - y = 0$.Let the point be $P(0, 1)$. The formula for the reflection $(x', y')$ of a point $(x_0, y_0)$ in the line $a

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Statement-$1$ and Statement-$2$ are both true and Statement-$2$ is the correct explanation of Statement-$1$.

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(A) The line $L$ is given by $2x - y = 0$.Let the point be $P(0, 1)$. The formula for the reflection $(x', y')$ of a point $(x_0, y_0)$ in the line $ax + by + c = 0$ is $\frac{x' - x_0}{a} = \frac{y' - y_0}{b} = -2 \frac{ax_0 + by_0 + c}{a^2 + b^2}$.Substituting $a = 2, b = -1, c = 0$ and $(x_0, y_0) = (0, 1)$:$\frac{x' - 0}{2} = \frac{y' - 1}{-1} = -2 \frac{2(0) - 1(1) + 0}{2^2 + (-1)^2} = -2 \frac{-1}{5} = \frac{2}{5}$.So,$x' = 2 	imes \frac{2}{5} = \frac{4}{5}$ and $y' - 1 = -1 	imes \frac{2}{5} = -\frac{2}{5} \implies y' = 1 - \frac{2}{5} = \frac{3}{5}$.Thus,Statement-$1$ is true.Statement-$2$ describes the definition of reflection,which is that the line $L$ is the perpendicular bisector of the segment joining the point and its reflection. Therefore,the points are equidistant from the line and lie on opposite sides. Thus,Statement-$2$ is true and is the correct explanation for Statement-$1$.

Let $L$ be the line $y = 2x$ in two dimensions.
Statement-$1$: The reflection of the point $(0, 1)$ in $L$ is the point $(4/5, 3/5)$.
Statement-$2$: The points $(0, 1)$ and $(4/5, 3/5)$ lie on opposite sides of the line $L$ and are equidistant from it.

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Let $L$ be the line $y = 2x$ in two dimensions.Statement-$1$: The reflection of the point $(0, 1)$ in $L$ is the point $(4/5, 3/5)$.Statement-$2$: The points $(0, 1)$ and $(4/5, 3/5)$ lie on opposite sides of the line $L$ and are equidistant from it.