Answer
The midpoint of the hypotenuse of a right triangle is always an equal distance away from each of the vertices.
Work Step by Step
We call the vertices:
$(0,0); (0,2b); (0,2a)$
Since the midpoint is on one side, we find that it is already known to be $d= \sqrt{b^2 +a^2} $ away from each vertex touching the hypotenuse. We use the distance formula from the origin to find:
$d_2 =\sqrt{a^2+b^2}$
The two distances are equal.
