# Figure ABCD is a trapezoid with point A (0, -4).

Figure ABCD is a trapezoid with point A (0, -4). What rule would rotate the figure 270° clockwise?

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Philip O'Neill
The objective here is to tell the rule to rotate the co-ordinate point (0, -4) by an angle of 270° clockwise.
A point (x, y) in coordinate plane is rotated by an angle θ clockwise is given by the rotation matrix
$\begin{bmatrix}\cos\theta&\sin\theta\\-\sin\theta&\cos\theta\end{bmatrix}$
Here, $$\displaystyle\theta={270}^{\circ}$$
$\begin{bmatrix}\cos270&\sin270\\-\sin270&\cos270\end{bmatrix}$
Thus, the rule to rotate the co-ordinate point (0, -4) by an angle of 270° clockwise is given by:
$\begin{bmatrix}x\\y\end{bmatrix}=\begin{bmatrix}\cos270&\sin270\\-\sin270&\cos270\end{bmatrix}\begin{bmatrix}0&4\end{bmatrix}$
$\begin{bmatrix}x\\y\end{bmatrix}=\begin{bmatrix}0\cos270+4\sin270\\-0\sin270+4\cos270\end{bmatrix}$
$\begin{bmatrix}x\\y\end{bmatrix}=\begin{bmatrix}4\sin270\\4\cos270\end{bmatrix}$