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

Jason Watson 2021-11-22 Answered
Figure ABCD is a trapezoid with point A (0, -4). What rule would rotate the figure 270° clockwise?

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Expert Answer

Philip O'Neill
Answered 2021-11-23 Author has 0 answers
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:
\[\begin{bmatrix}x\\y\end{bmatrix}=\begin{bmatrix}\cos270&\sin270\\-\sin270&\cos270\end{bmatrix}\begin{bmatrix}0&4\end{bmatrix}\]
\[\begin{bmatrix}x\\y\end{bmatrix}=\begin{bmatrix}0\cos270+4\sin270\\-0\sin270+4\cos270\end{bmatrix}\]
\[\begin{bmatrix}x\\y\end{bmatrix}=\begin{bmatrix}4\sin270\\4\cos270\end{bmatrix}\]
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