If the vertices of triangle pqr are p(2,2) q(8,4) r(3,7), find the equation of the perpendicular bisector of segment pq

First off, let's find the slope of PQ



now, a perpendicular line to PQ, will have a negative reciprocal slope, thus



now, we also know that, the line is a bisector of PQ, therefore, it cuts PQ in two equal halves, so it passes half-way through PQ, what is that point anyway?



so then, what's the equation of a line whose slope is -1/3 and runs through 5,3?

What is the inequality?