A line $L$ is the perpendicular bisector of the line segment joining points $P(4,6)$ and $Q(10,2)$. What is the y-intercept of line $L$?

Question

Accepted Answer

- 6.5. The midpoint of $P(4,6)$ and $Q(10,2)$ is $(7,4)$. The slope of $PQ$ is $(2-6)/(10-4)=-4/6=-2/3$, so the perpendicular slope is $3/2$. Using point-slope form through $(7,4)$, the line is $y-4=\frac{3}{2}(x-7)$, giving $y=-\frac{13}{2}=-6.5$ when $x=0$.

A line \(L\) is the perpendicular bisector of the line segment joining points \(P(4,6)\) and \(Q(10,2)\). What is the y-intercept of line \(L\)?

Solution

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