Perpendicular Bisector: Understanding the Wording

[Yazan975]

View attachment 8416

I know that when two lines are perpendicular their gradients multiply to -1 but I don't get the wording here.
Any suggestions?

 

[HOI]

The line through (1, 2) and (-5, -4) has slope $\frac{-5- 1}{-4- 2}= \frac{-6}{6}= 1$ so any line perpendicular to that has slope -1. Further the perpendicular **bisector** goes through the point exactly half way between (1, 2) and (-5, 4) which is $\left(\frac{1+ (-5)}{2}, \frac{2+ 4}{2}\right)$$= \left(\frac{-4}{2},\frac{6}{3}\right)= (-2, 3)$.

What is the equation of the line through (-2, 3) with slope -1?