Answer:
Given a triangle ABC, Pythagoras' Theorem shows that:
[tex]c^2=a^2+b^2[/tex]
Thus,
[tex]c = \sqrt{a^2+b^2}[/tex]
The distance formula, gives an equivalent expression based on two points at the end of the hypotenuse for a triangle.
[tex]d^2 = (x_{2} -x_{1})^2 + (y_{2} -y_{1})^2[/tex]
[tex]d = \sqrt{(x_{2}-x_{1})^2 + (y_{2} -y_{1})^2 }[/tex]
Therefore when given the hypotenuse with endpoints at
[tex](x_{1}, y_{1}) and {(x_{2}, y_{2})[/tex]
We know that the third point of the right triangle will be at
[tex](x_{2}, y_{1})[/tex]
and that the two side lengths will be defined by the absolute values of:
[tex](x_{2} - x_{1}) = a[/tex]
[tex](y_{2} - y_{1}) = b[/tex]
