Answer
A) The midpoint is equidistant from the first two vertices by the definition of a midpoint. We now draw a second congruent right triangle touching the first triangle. Since congruent diagonals of rectangles bisect each other, it follows that the third midpoint is the same distance away as the first.
B) 5
Work Step by Step
A) We proved this by drawing a second triangle and then using relationships for rectangles to show that the three distances are the same.
B) The length to the midpoint is half the length of the hypotenuse. The hypotenuse length is:
$$ = .5 \sqrt{6^2 + 8^2 } \\ =.5 \sqrt{100} = 5$$
