Let L be the line y = 2x in the two-dimension | vedclass

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(C) Let $P(0, 1)$ be the given point and $L: 2x - y = 0$ be the line.The formula for the image $(x_1, y_1)$ of a point $(x_0, y_0)$ in the line $ax +

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Statement $1$ is true,Statement $2$ is true,Statement $2$ is a correct explanation for Statement $1$.

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(C) Let $P(0, 1)$ be the given point and $L: 2x - y = 0$ be the line.The formula for the image $(x_1, y_1)$ of a point $(x_0, y_0)$ in the line $ax + by + c = 0$ is given by $\frac{x_1 - x_0}{a} = \frac{y_1 - y_0}{b} = -2 \frac{ax_0 + by_0 + c}{a^2 + b^2}$.Substituting the values: $\frac{x_1 - 0}{2} = \frac{y_1 - 1}{-1} = -2 \frac{2(0) - 1(1)}{2^2 + (-1)^2} = -2 \frac{-1}{5} = \frac{2}{5}$.Thus,$x_1 = 2 	imes \frac{2}{5} = \frac{4}{5}$ and $y_1 = 1 - \frac{2}{5} = \frac{3}{5}$.So,Statement $1$ is true.By definition,the image of a point in a line is the point such that the line is the perpendicular bisector of the segment joining the point and its image. This implies the points lie on opposite sides and are equidistant from the line. Thus,Statement $2$ is true and is the correct explanation for Statement $1$.

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