Wednesday

July 30, 2014

July 30, 2014

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

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 5:25amOne 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.

**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 - what is the orthocenter of triangle with the vertices of X(-11,0), Y...

Geometry PLEASE HELP ME - ABC has vertices A(0, 6), B(4, 6), and C(1, 3). Sketch...

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 ...

pre-calculus - triangle KLM has vertices K(0,0), L(18,0), and M(6,12). a. Write ...

Geometry - I need help with vertices! The vertices of triangle FGH are F(1,1), G...