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 $PM$ is perpendicular to the line $x+y=3$,the slope of $PM$ is the negative reciprocal of the slo

Vedclass · Accepted Answer

$(1, 2)$

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(C) Let the coordinates of $M$ be $(x_1, y_1)$.Since $PM$ is perpendicular to the line $x+y=3$,the slope of $PM$ is the negative reciprocal of the slope of the given line.The slope of $x+y=3$ is $-1$,so the slope of $PM$ is $1$.Thus,$\frac{y_1-3}{x_1-2} = 1$ $\Rightarrow y_1-3 = x_1-2$ $\Rightarrow x_1-y_1 = -1$ (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. $ii$: $(x_1-y_1) + (x_1+y_1) = -1+3$ $\Rightarrow 2x_1 = 2$ $\Rightarrow x_1 = 1$.Substituting $x_1=1$ into Eq. $ii$: $1+y_1=3 \Rightarrow y_1=2$.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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