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.

Answer:The coordinates of the vertices of the reflected figure are :R' is (-3 , -7), S' is (5 , -3), T' is (6 , 5) ⇒the right answer is figure (a)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}{cc}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}{cc}-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 x-axis  by each point to find the image of each point- The dimension of the matrix of the reflection across the x-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)∴ [tex]R'=\left[\begin{array}{cc}1&0\\0&-1\end{array}\right]\left[\begin{array}{c}-3\\7\end{array}\right]=[/tex]   [tex]\left[\begin{array}{c}(1)(-3)+(0)(7)\\(0)(-3)+(-1)(7)\end{array}\right]=\left[\begin{array}{c}-3\\-7\end{array}\right][/tex]∴ R' is (-3 , -7)∵ Point S is (5 , 3)∴ [tex]S'=\left[\begin{array}{cc}1&0\\0&-1\end{array}\right]\left[\begin{array}{c}5\\3\end{array}\right]=[/tex]    [tex]\left[\begin{array}{c}(1)(5)+(0)(3)\\(0)(5)+(-1)(3)\end{array}\right]=\left[\begin{array}{c}5\\-3\end{array}\right][/tex]∴ S' is (5 , -3)∵ Point T is (6 , -5)∴ [tex]T'=\left[\begin{array}{cc}1&0\\0&-1\end{array}\right]\left[\begin{array}{c}6\\-5\end{array}\right]=[/tex]    [tex]\left[\begin{array}{c}(1)(6)+(0)(-5)\\(0)(6)+(-1)(-5)\end{array}\right]=\left[\begin{array}{c\pi }6\\5\end{array}\right][/tex]∴ T' is (6 , 5)* Look to the answer and find the correct figure- In figure (d) R' is (-3 , -7), S' is (5 , -3), T' is (6 , 5)∴ The right answer is figure (a)