Answer
$y=-2x+9$
Work Step by Step
$Q= (x_{1},y_{1})=(\frac{1+5}{2},\frac{2+4}{2})=(3,3)$
Slope of the segment= $\frac{4-2}{5-1}=\frac{1}{2}$
Slope of perpendicular bisector m= $\frac{-1}{slope\,of\,the\,segment}=\frac{-1}{\frac{1}{2}}=-2$
Equation of a line in point-slope form is
$y-y_{1}=m(x-x_{1})$
Plugging in the values, we have
$y-3=-2(x-3)$
or $y=-2x+9$
