9514 1404 393
Answer:
(-2, 2)
Explanation:
The orthocenter is the intersection of the altitudes. The altitude lines are not difficult to find here. Each is a line through the vertex that is perpendicular to the opposite side.
Side XZ is horizontal, so the altitude to that side is the vertical line through Y. The x-coordinate of Y is -2, so that altitude has equation ...
x = -2
__
Side YZ has a rise/run of -1/1 = -1, so the altitude to that side will be the line through X with a slope of -1/(-1) = 1. In point-slope form, the equation is ...
y -(-1) +(1)(x -(-5))
y = x +4 . . . . . . . . subtract 1 and simplify
The orthocenter is the point that satisfies both these equations. Using the first equation to substitute for x in the second, we have ...
y = (-2) +4 = 2
The orthocenter is (x, y) = (-2, 2).