91Ó°ÊÓ

Types of transformation are

• Translation- When figure in moved from one location to another location without changing its size shape or orientation.
• Dilation- When figure is reduced or enlarged.
• Reflection- When every point of a figure is mapped to a corresponding image across a line of symmetry.
• Rotation- when a figure is moved around a centre point, usually origin.

As given image is moved around a origin, so given transformation is rotation.

To determine the vertices of image multiply the rotation matrix with vertex matrix of given image

Common rotation matrix are

Multiply vertex matrix of pre-image with rotation matrices and compare it with vertex matrix of image

$\begin{array}{c}\left[\begin{array}{cc}0& −1\\ 1& 0\end{array}\right]×\left[\begin{array}{cccc}2& 4& 2& −3\\ 3& −3& −5& −2\end{array}\right]=\left[\begin{array}{cccc}−3& 3& 5& 2\\ 2& 4& 2& −3\end{array}\right]\left(1\right)\\ \left[\begin{array}{cc}−1& 0\\ 0& −1\end{array}\right]×\left[\begin{array}{cccc}2& 4& 2& −3\\ 3& −3& −5& −2\end{array}\right]=\left[\begin{array}{cccc}−2& −4& −2& 3\\ −3& 3& 5& 2\end{array}\right]\left(2\right)\\ \left[\begin{array}{cc}0& 1\\ −1& 0\end{array}\right]×\left[\begin{array}{cccc}2& 4& 2& −3\\ 3& −3& −5& −2\end{array}\right]=\left[\begin{array}{cccc}3& −3& −5& −2\\ −2& −4& −2& 3\end{array}\right]\left(3\right)\end{array}$

As vertex matrix in product (2) is same as the vertex matrix of image.

So, pre-image is rotated $180°$ counter clockwise.