A triangle has corners A, B, and C located at #(4 ,2 )#, #(1 ,3 )#, and #(6 ,5 )#, respectively. What are the endpoints and length of the altitude going through corner C?
1 Answer
Explanation:
From the diagram:
We need to find the endpoints of the altitude passing through
Using point
Using point slope form of a line and point
We now need the equation of the line through point
If two line are perpendicular the the product of their gradients is
Let the unknown gradient be
Using this and point
We solve now solve
Substitute in
So the end points of the altitude are:
The length of the altitude line