How hypotenuse is twice the length of median that joins it by using coordinate formula

Answer 1

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.