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.
Answer This Question
Related Questions
 Orthocenter Question  Triangle ABC has vertices A(0,6), B(4,6) and C(1,3) Find ...
 Geometry  how do you find the orthocenter of a triangle with the vertices A(4,0...
 Geometry  Find the coordinates of the orthocenter of the triangle with the ...
 Geometry PLEASE HELP ME  ABC has vertices A(0, 6), B(4, 6), and C(1, 3). Sketch...
 geometry  what is the orthocenter of triangle with the vertices of X(11,0), Y...
 Algebra  I'm stuck!! Can someone please help me with this problem?? A triangle ...
 geometry  Triangle PQR has vertices P(1,2), Q(25,2) and R(10,20). Find the ...
 geometry  Please use this for the portfolio. You will need graph paper. 1. ...
 analytic geometry/graphing problem  The vertices of a triangle are the points ...
 precalculus  triangle KLM has vertices K(0,0), L(18,0), and M(6,12). a. Write ...
More Related Questions