Answer
See the explanation below.
Work Step by Step
Let $u=(-1,4)$ and $v=(8,2)$; then we have:
(a) Since $$u\cdot v=-8+8=0,$$ then the set is orthogonal.
(b) To normalize the set, we have $$u_1=\frac{1}{\|u\|}u=\frac{1}{\sqrt{17}}(-1,4),$$ $$v_1=\frac{1}{\|v\|}v=\frac{1}{\sqrt{68}}(8,2).$$ Now, the set $\{u_1,v_1\}$ is an orthonormal set.
