questn

I'm assuming that the 90° rotation is counter-clockwise

Look at the graph, here.......https://www.desmos.com/calculator/lytpjurgg5

The 90° rotation produces a second point at (-3,1)

When this point is reflected across the y axis, the coordinates of the final image are,  (3,1)

the point (1,3) is rotated 90 degrees about the origin and then reflected across the y- axis. What are the coordinators of the image?

$\begin{array}{lcll} \text{Rotation counter clockwise }90^{\circ}:\\ \begin{pmatrix} \cos{(90^{\circ})} & \sin{(90^{\circ})} \\ -\sin{(90^{\circ})} & \cos{(90^{\circ})} \end{pmatrix} &=& \begin{pmatrix} 0 & 1 \\ -1 & 0 \end{pmatrix}\\\\ \text{Refection y-axis}:\\ &=& \begin{pmatrix} -1 & 0 \\ 0 & 1 \end{pmatrix}\\\\ \text{Rotation counter clockwise }90^{\circ} \times \text{Reflection y-axis}:\\ \begin{pmatrix} 0 & 1 \\ -1 & 0 \end{pmatrix} \cdot \begin{pmatrix} -1 & 0 \\ 0 & 1 \end{pmatrix} &=& \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}\\\\ \text{Point} (x_p,y_p) \times \text{ Rotation counter clockwise }90^{\circ} \times \text{Reflection y-axis}:\\ ( x_p, y_p ) \cdot \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix} &=& ( y_p, x_p ) \\\\ \text{Point} (1,3) \times \text{ Rotation counter clockwise }90^{\circ} \times \text{Reflection y-axis}:\\ ( 1, 3 ) \cdot \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix} &=& ( 3, 1 ) \\\\ \end{array}$

change x and y $\Rightarrow$ Reflection at line y = x