The line represents the width of your face, with as your right eye. is the reflection of your face in the mirror, which lies along the line .
Then it is well known that the distances of the object and its reflection from the mirror are equal. SoA ray of light from hits the mirror at and is reflected into your eye, , producing an image of at . So is a straight line, with the apparent point on the mirror of the position of .
Similarly for : this is the apparent point on the mirror of the position of .
By similar triangles, since , we can easily prove that .