9514 1404 393
Answer:
(4, -1)
Step-by-step explanation:
The orthocenter is the intersection of altitudes. Each altitude is the line through a vertex and perpendicular to the opposite side of the triangle.
It is useful to plot the points on a graph. This shows you segment KM is a horizontal line, so one altitude line is x=4, the vertical line through point L.
The graph also shows you segment KL has a rise of 8 for a run of 2, so a slope of rise/run = 8/2 = 4. Then the altitude perpendicular to that side will have slope -1/4 (the opposite reciprocal of 4), and will go through point M(8, -2). In point-slope form, the equation of the altitude through M can be written ...
y -k = m(x -h) . . . . . . . line with slope m through point (h, k)
y +2 = -1/4(x -8)
We want to find the y-coordinate of the point of intersection of this line with the line x=4. We can substitute x=4 and solve for y.
y +2 = -1/4(4 -8) . . . . . . substitute x=4
y = 1 -2 . . . . . . . . . . simplify and subtract 2
y = -1
The orthocenter for the given triangle has coordinates (4, -1).
