Transformation is the set of new mathematical coordinates declared to be different functions of the original coordinates.The image of point A will be [tex]\left[\begin{array}{ccc}-4\\2\end{array}\right][/tex].
What is the transformation of a point?
The transformation can be defined as the introduction of a new set of mathematical coordinates that are declared to be different functions of the original coordinates.
To get the image of any transformation under the certain matrix is given by the formula,
Matrix of transformation × object = Image
As we can see object A is at (2,4), while the transformation matrix is given as,
[tex]\left[\begin{array}{ccc}0&-1\\1&0\end{array}\right] \times \left[\begin{array}{ccc}2\\4\end{array}\right] = \left[\begin{array}{ccc}0+-4\\2+0\end{array}\right] = \left[\begin{array}{ccc}-4\\2\end{array}\right][/tex]
Hence, the image of point A will be [tex]\left[\begin{array}{ccc}-4\\2\end{array}\right][/tex].
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