What is the altitude?

Question

Triangle ABC has vertices A(3,4), B(-5,2), and C(1,-4). Determine the equation of AE, the altitude from A to BC.

Answer 1

By definition the altitude AE is perpendicular to BC.

The slope of BC is -1.  

The slope of AE is 1 (negative reciprocal of -1)

Substituting x and y from point A  and the slope of 1 you can solve for the y intercept of line AE. 

The resulting equation is y = x + 1.

 

If you would like you can then determine the equation for line BC.  Solve the system of equations that represent AE and BC to find the point E.  That would be for extra credit.