Provide an Appropriate Response $\left| \frac { a + b } { 2 } \right| = \left| \frac { a - b } { 2 } \right|$

Essay

Provide an appropriate response.
-Show that the midpoint of the hypotenuse of a right triangle is equidistant from all three vertices. [Hint: See the figure below. Show that $\left| \frac { a + b } { 2 } \right| = \left| \frac { a - b } { 2 } \right|$ .]