Question:

The equations of two adjacent sides of a rhombus are $\displaystyle y= 2x + 4 $, $\displaystyle -\frac{1}{3}x +4$. If (12,0) is one vertex and all vertices have positive coordinates, find the coordinates of other three vertices.

My attempt:

the other vertex i found is (0,4)

the distance between (0,4) and (12,0) = $\displaystyle 4\sqrt{10}$

the equation of the line that passes through (12,0) is $\displaystyle y = 2x -24 $

the problem is how to form the other equation in order to find the other vertices

please help