geometry
posted by Megan on .
I'm so confused...can someone please help???
I need to find the orthocenter of the triangle with the vertices R(4,8), S(1,5), T(5,5)???
How do you get 'y' for this problem?

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 (58)/(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).
(y5)/(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.