If PM is the perpendicular from P(2, 3) onto | vedclass

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(C) Let the coordinates of $M$ be $(x_1, y_1)$.Since the line $PM$ is perpendicular to the given line $x + y = 3$,the slope of $PM$ is the negative re

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$(1, 2)$

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(C) Let the coordinates of $M$ be $(x_1, y_1)$.Since the line $PM$ is perpendicular to the given line $x + y = 3$,the slope of $PM$ is the negative reciprocal of the slope of the line $x + y = 3$.The slope of $x + y = 3$ is $-1$,so the slope of $PM$ is $1$.Thus,$\frac{y_1 - 3}{x_1 - 2} = 1 \implies y_1 - 3 = x_1 - 2 \implies x_1 - y_1 = -1$ (Eq. $i$).Since $M(x_1, y_1)$ lies on the line $x + y = 3$,we have $x_1 + y_1 = 3$ (Eq. $ii$).Adding Eq. $i$ and Eq. $ii$: $(x_1 - y_1) + (x_1 + y_1) = -1 + 3 \implies 2x_1 = 2 \implies x_1 = 1$.Substituting $x_1 = 1$ in Eq. $ii$: $1 + y_1 = 3 \implies y_1 = 2$.Therefore,the coordinates of $M$ are $(1, 2)$.

If $PM$ is the perpendicular from $P(2, 3)$ onto the line $x + y = 3$,then the coordinates of $M$ are

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