If (-2, 6) is the image of the point (4, 2) w | vedclass

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(A) Let the point $P = (-2, 6)$ and $Q = (4, 2)$. The line $L = 0$ is the perpendicular bisector of the segment $PQ$.The midpoint of $PQ$ is $\left( \

Vedclass · Accepted Answer

$3x - 2y + 5 = 0$

Vedclass · Answer

(A) Let the point $P = (-2, 6)$ and $Q = (4, 2)$. The line $L = 0$ is the perpendicular bisector of the segment $PQ$.The midpoint of $PQ$ is $\left( \frac{-2 + 4}{2}, \frac{6 + 2}{2} \right) = (1, 4)$.The slope of $PQ$ is $m_{PQ} = \frac{2 - 6}{4 - (-2)} = \frac{-4}{6} = -\frac{2}{3}$.Since line $L$ is perpendicular to $PQ$,its slope $m_L$ is the negative reciprocal of $m_{PQ}$,so $m_L = \frac{3}{2}$.The equation of line $L$ passing through $(1, 4)$ with slope $\frac{3}{2}$ is given by:$y - 4 = \frac{3}{2}(x - 1)$$2(y - 4) = 3(x - 1)$$2y - 8 = 3x - 3$$3x - 2y + 5 = 0$.

If $(-2, 6)$ is the image of the point $(4, 2)$ with respect to line $L = 0$,then $L =$

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