What is the orthocenter of a triangle with corners at #(3 ,1 )#, #(1 ,6 )#, and (5 ,2 )#?
Triangle with vertices at
We have three vertices:
We will find the slope using the vertices
Formula to find the slope (m) =
We need a perpendicular line from the vertex
Perpendicular slope is
Use the Point-Slope Formula to find the equation.
We will repeat the process from
Next, we find the slope.
Find the perpendicular slope.
Find the solution to the system of linear equations to find the vertices of the Orthocenter of the triangle.
The solution is becoming too long. Method of Substitution will provide solution for the system of linear equations.
The construction of the triangle with the Orthocenter is: