geometry
posted by Megan .
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.
Respond to this Question
Similar Questions

precalculus
triangle KLM has vertices K(0,0), L(18,0), and M(6,12). a. Write equations for the altitudes to the three sides of the triangle. b. Show that the altitudes intersect at a single point O, called the orthocenter of the triangle. 
geometry
Triangle PQR has vertices P(1,2), Q(25,2) and R(10,20). Find the coordinates of the centroid. Find the coordinates of the circumcenter. Find the coordinates of the orthocenter. Find the equation of the line. 
geometry
what is the orthocenter of triangle with the vertices of X(11,0), Y(11,8), Z(1,4)? 
Geometry
how do you find the orthocenter of a triangle with the vertices A(4,0) B(2,4) C(0,6)? 
Orthocenter Question
Triangle ABC has vertices A(0,6), B(4,6) and C(1,3) Find the orthocenter of triangle ABC. Please show your work so that I can understand how to do this type of problem. Thank You I really appreciate your help ^_^ 
Geometry PLEASE HELP ME
ABC has vertices A(0, 6), B(4, 6), and C(1, 3). Sketch a graph of ABC and use it to find the orthocenter of ABC. Then list the steps you took to find the orthocenter, including any necessary points or slopes you had to derive. 
analytic geometry/graphing problem
The vertices of a triangle are the points of intersection of the line y=x1, x=2 and y = 1/5x + 13/5. Find an equation of the circle passing through all three vertices. I don't understand how to solve this: should I set them all equal … 
Algebra
I'm stuck!! Can someone please help me with this problem? 
geometry
Please use this for the portfolio. You will need graph paper. 1. Start with Triangle ABC with vertices: A(0,2), B(2,5), C(3,0) 2. Find slope of side AB and BC 3. Now TRANSLATE the Triangle 4 units left, and 2 units up (x4,y+2) and … 
Geometry
Find the coordinates of the orthocenter of the triangle with the given vertices. L (8,0) M (10,8) N (14,0)