How hypotenuse is twice the length of median that joins it by using coordinate formula
set it up so that the three vertices are at
(0,0), (a,0), (0,b)
Then the median to the hypotenuse has endpoint (a/2,b/2)
So, its length
√((a/2)^2 + (b/2)^2)
= √(a^2/4 + b^2/4)
= 1/2 √(a^2+b^2)
which is half the hypotenuse.