The vertices of the original quadrilateral can be written in matrix form using the vertex matrix. The vertex matrix is
[tex]\begin{pmatrix}-5&-1&-3&-7\\ 4&-1&-6&-3\end{pmatrix}[/tex]
To find the coordinates of the endpoints or vertices of the image of the given coordinate points reflected about the y-axis, we just need to multiply the transformation matrix by the vertex matrix. The transformation matrix for this particular problem is
[tex]\begin{pmatrix}-1&0\\ 0&1\end{pmatrix}[/tex]
Multiplying the two matrices, we have
[tex]\begin{pmatrix}-1&0\\ 0&1\end{pmatrix}\begin{pmatrix}-5&-1&-3&-7\\ 4&-1&-6&-3\end{pmatrix}=\begin{pmatrix}5&1&3&7\\ 4&-1&-6&-3\end{pmatrix}[/tex]
Therefore, the coordinates of the endpoints or vertices of the image are (5,4), (1,-1), (3, -6) and (7, -3).
