Posted by Megan on Monday, November 21, 2011 at 8:27pm.
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?

geometry  Steve, Tuesday, November 22, 2011 at 5:25am
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.