Triangle Perimeter – Minimize it!

The puzzle below shows a triangle.  One of the vertices is fixed at (7,1), one of them is fixed on the graph of the line y = x, and one of them is fixed on the x-axis.  Where should the two free points be placed so that the triangle has the lowest perimeter?

The perimeter is displayed in the upper left corner.  Above that there are two checkboxes that can be used to show the lengths of the triangle’s individual sides as well as some relevant angle measurements.