Find the coordinates of the orthocenter of each triangle with the given vertices.
j(3, -2), k(5,6), l(9,-2)
my geometry teacher said the correct answer is (5,-1), but i'm not entirely sure how to solve it myself.

First you should plot the points and connect them so you can see the triangle. 

Then you need to find the slope of each line segment. Then you need to get the slope that would be perpendicular to each individual slope. 

Then you got to the OPPOSITE vertex of each line segment, and use the perpendicular slope from that vertex to draw a line, then you will see that all 3 of them intersect at (5,-1)