1. rhombus question

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

Let $(x_1,y_1)$ and $(x_2,y_2)$ be the other two rhombus vertices.
distance between $(12,0)$ and $(x_1,2x_1-24)$ is $4\sqrt{10}$
distance between $(0,4)$ and $(x_2,2x_2+4)$ is also $4\sqrt{10}$