If is the frontier of the triangle with vertices , and , show that without calculating the integral.

My attempt : I drew the sketch of .

Then I wrote .

I also wrote that , hence I'm done if I show that for . (Correct me please if I'm wrong saying that , where denotes the frontier of the triangle.)

Here's where I'm stuck. I thought about calculating the image of the interior of the triangle under the transformation but I believe this is a long work. Also it wouldn't finish there. I believe I'm missing something obvious.