Use matrices to determine the coordinates of the vertices of the reflected figure. Then graph the pre-image and the image on the same coordinate grid. (Picture below)

Answer:The coordinates of the vertices of the reflected figure are :R' is (3 , 7), S' is (-7 , 2), T' is (-5 , -3) ⇒the right answer is figure (d)Step-by-step explanation:* Lets study the matrices of the reflection- The matrix of the reflection across the x-axis is  [tex]\left[\begin{array}{ccc}1&0\\0&-1\end{array}\right][/tex]- Because when we reflect any point across the x-axis we  change the sign of the y-coordinate- The matrix of the reflection across the y-axis is   [tex]\left[\begin{array}{ccc}-1&0\\0&1\end{array}\right][/tex]- Because when we reflect any point across the y-axis we  change the sign of the x-coordinate* Now lets solve the problem- We will multiply the matrix of the reflection across the y-axis  by each point to find the image of each point- The dimension of the matrix of the reflection across the y-axis  is 2×2 and the dimension of the matrix of each point is 2×1, then the dimension of the matrix of each image is 2×1∵ Point R is (-3 , 7)∴ R' = [tex]\left[\begin{array}{ccc}-1&0\\0&1\end{array}\right] \left[\begin{array}{ccc}-3\\7\end{array}\right]=[/tex]   [tex]\left[\begin{array}{ccc}(-1)(-3)+(0)(7)\\(0)(-3)+(1)(7)\end{array}\right]=\left[\begin{array}{ccc}3\\7\end{array}\right][/tex]∴ R' is (3 , 7)∵ Point S is (7 , 2)∴ S' = [tex]\left[\begin{array}{ccc}-1&0\\0&1\end{array}\right]\left[\begin{array}{ccc}2\\7\end{array}\right]=[/tex]    [tex]\left[\begin{array}{ccc}(-1)(7)+(0)(2)\\(0)(7)+(1)(2)\end{array}\right]=\left[\begin{array}{ccc}-7\\2\end{array}\right][/tex]∴ S' is (-7 , 2)∵ Point T is (5 , -3)∴ T' = [tex]\left[\begin{array}{ccc}-1&0\\0&1\end{array}\right]\left[\begin{array}{ccc}5\\-3\end{array}\right]=[/tex]    [tex]\left[\begin{array}{ccc}(-1)(5)+(0)(-3)\\(0)(5)+(1)(-3)\end{array}\right]=\left[\begin{array}{ccc}-5\\-3\end{array}\right][/tex]∴ T' is (-5 , -3)* Look to the answer and find the correct figure- In figure (d) R' is (3 , 7), S' is (-7 , 2), T' is (-5 , -3)∴ The right answer is figure (d)