Answer
a) $10; 3; \sqrt{109};$
b) The three sides verify the Pythagorean Theorem.
Work Step by Step
a) Find the length of each side of the right triangle:
$\sqrt{[9-(-1)]^2+(1-1)^2}=\sqrt{100}=10$
$\sqrt{(9-9)^2+(4-1)^2}=\sqrt{9}=3$
$\sqrt{[9-(-1)]^2+(4-1)^2}=\sqrt{109}$
b) Check that the sides verify the Pythagorean Theorem:
$10^2+3^2\stackrel{?}{=}(\sqrt{109})^2$
$100+9\stackrel{?}{=}109$
$109=109\checkmark$
