# Math Help - rotations of points

1. ## rotations of points

Hi Can anyone explain this following example to me? I have no idea how they obtained those new coordinates. How exactly do I multiply the point A by the rotation matrix?
Thanks

2. Originally Posted by srose34
Hi Can anyone explain this following example to me? I have no idea how they obtained those new coordinates. How exactly do I multiply the point A by the rotation matrix?
Here is the result without matrices.
$\left( {x,y} \right) \to \left( {x',y'} \right)$ by the system:
$\left\{ \begin{gathered}
x' = x\cos (\varphi ) - y\sin (\varphi ) \hfill \\
y' = x\sin (\varphi ) + y\cos (\varphi ) \hfill \\
\end{gathered} \right.$
.

3. Hi
I tried that method but my numbers are the wrong way around e.g (root(2), 0) instead of (0, root(2))

4. Originally Posted by srose34
Hi
I tried that method but my numbers are the wrong way around e.g (root(2), 0) instead of (0, root(2))
Check your algebra.
$\left\{ \begin{gathered}
x' = 1\frac{{\sqrt 2 }}
{2} - 1\frac{{\sqrt 2 }}
{2} = 0 \hfill \\
y' = 1\frac{{\sqrt 2 }}
{2} + 1\frac{{\sqrt 2 }}
{2} = \sqrt 2 \hfill \\
\end{gathered} \right.
$

5. ok, thanks I see what I was doing wrong