Why is $2{\vec d\cdot \vec m\over \vec m\cdot \vec m}\vec m-\vec d=(0,1)$?

Question

How do we calculate $$2{\vec d\cdot \vec m\over \vec m\cdot \vec m}\vec m-\vec d$$

given the data ${\vec d = (1, 0)}$ and ${\vec m = (1, 1)}$?

The answer should be $(0, 1)$, but I don't know why.

Answer 1

We have: $2\cdot \frac{\binom{1}{0} \cdot \binom{1}{1}}{\binom{1}{1} \cdot \binom{1}{1}}\binom{1}{1} - \binom{1}{0}$ = $ 2\cdot \frac{1\cdot 1+0\cdot 1}{1\cdot 1+1\cdot 1} \binom{1}{1} - \binom{1}{0}$ = $\binom{1}{1} - \binom{1}{0} = \binom {0}{1}$

Answer 2

$$2{\vec d\cdot \vec m\over \vec m\cdot \vec m}\vec m-\vec d=2\cdot\frac{1}{2}\vec m-\vec d =\vec m-\vec d=(0,1)$$