Posted by Megan on Monday, November 21, 2011 at 8:27pm.
One way to solve this problem is to think of the altitudes from R,S,T to the opposite side. For each of these lines, we have a point and a slope (perpendicular to the line forming the opposite side)
So, a nice easy place to start is to notice that ST is a horizontal line. So, the altitude from R is the line
x = -4
Now, if we find where another altitude intersects that line, we are done.
The slope of RT is (5-8)/(5+4) = -3/9 = -1/3
The altitude from S to RT will have slope 3.
So, now we have a point (-1,5) and a slope (3).
(y-5)/(x+1) = 3
y = 3x + 8
That intersects x=-4 at y=4
So, the orthocenter is at (-4,4)
If you want, you can verify by checking the other altitudes.
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