# What is the orthocenter of the triangle formed by the intersection of the lines #x = 4# , #y = 1/2x + 7# , and# y = -x + 1#?

##### 1 Answer

#### Answer:

The Orthocenter, O is

#### Explanation:

The orthocenter is the point where all three altitudes of the triangle intersect. An altitude is a line which passes through a vertex of the triangle and is perpendicular to the opposite side. So we need to find lines that are perpendicular to the give equation and where at least 2 of them intersect:

A perpendicular line to any line,

First we need to get the coordinates of the vertices,

Let's solve equations:

Given

Thus the vertices of the triangle are given by:

Now let find the perpendicular line to

So what we have is

and the line perpendicular to x=4 passing through A(-4,5) is

Thus the Orthocenter is