∆ABC has vertices: (0,0) , (12,6) , (18,0). Find the equations of the lines that contain the three altitudes of the triangle.

Question

∆ABC has vertices: (0,0) , (12,6) , (18,0). Find the equations of the lines that contain the three altitudes of the triangle.

Answer 1

This is a little messy but not difficult.

The altitude from (12,6) is easy: x=6.

The slope from the origin to (12,6) is 1/2; the perpendicular will have slope -2 and go through

(18,0) => -2=y/(x-18).

The slope of the last side is easily seen to be -1 and the perpendicular will have slope 1 and go through the origin so:y=x.

Note that 2 of the altitudes will fall outside the triangle.