Question

give the coordinates of the image. r_(360°,o)(jklm) for j(-4,7), k(1,5), l(6,1), m(3,-9) j (type an ordered pair.)

Explanation:

Step1: Recall rotation rule

A rotation of 360° about the origin \(O\) of a point \((x,y)\) results in the same point. The rotation matrix for a rotation of \(\theta = 360^{\circ}\) about the origin is \(

$$\begin{bmatrix}\cos\theta&-\sin\theta\\\sin\theta&\cos\theta\end{bmatrix}$$

=

$$\begin{bmatrix}1&0\\0&1\end{bmatrix}$$

\). And \(

$$\begin{bmatrix}1&0\\0&1\end{bmatrix}$$

$$\begin{bmatrix}x\\y\end{bmatrix}$$

=

$$\begin{bmatrix}x\\y\end{bmatrix}$$

\).

Step2: Apply to point J

For point \(J(-4,7)\), after a 360 - degree rotation about the origin, the coordinates remain the same.

Answer:

\((-4,7)\)