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?

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1. Midpoint of P(4,6) and Q(10,2) is $M\left(\frac{4+10}{2},\frac{6+2}{2}\right)=M(7,4)."

2. Slope of PQ is $m_{PQ}=\frac{2-6}{10-4}=\!-\frac{2}{3}$.

3. Slope of the perpendicular bisector is $m=\frac{3}{2}$.

4. Line through $M(7,4)$: $y-4=\frac{3}{2}(x-7)$. Put $x=0$ to get $y=4-\frac{21}{2}=-\frac{13}{2}=-6.5$.

FINAL_ANSWER: b

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