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 provided)

Answer:The coordinates of the vertices of the reflected figure are :R' is (5 , -2) , S' is (3 , 5) , T' is (-7 , 6) ⇒ the right answer is (d)Step-by-step explanation:* When you reflect a point across the line y = x, the x-coordinate  and y-coordinate change their places. - If the point is (x , y) then its image is (y , x)* If you reflect over the line y = -x, the x-coordinate and y-coordinate  change their places and their signs- If the point is (x , y) then its image is (-y , -x)* Lets study the matrix of the reflection  about the line y = x- The matrix of the reflection about the line y = x is  [tex]\left[\begin{array}{cc}0&1\\1&0\end{array}\right][/tex]- Because the x-coordinate and y-coordinate change places. * Now lets solve the problem - We will multiply the matrix of the reflection about y = x  by each point to find the image of each point - The dimension of the matrix of the reflection about y = x  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 ∵ The point R is (-2 , 5)∴ [tex]R'=\left[\begin{array}{cc}0&1\\1&0\end{array}\right]\left[\begin{array}{cc}-2\\5\end{array}\right]=[/tex]   [tex]\left[\begin{array}{c}(0)(-2)+(1)(5)\\(1)(-2)+(0)(5)\end{array}\right]=\left[\begin{array}{c}5\\-2\end{array}\right][/tex]∴ R' is (5 , -2)∵ The point S is (5 , 3)∴ [tex]S'=\left[\begin{array}{cc}0&1\\1&0\end{array}\right]\left[\begin{array}{c}5\\3\end{array}\right]=[/tex]   [tex]\left[\begin{array}{c}(0)(5)+(1)(3)\\(1)(5)+(0)(3)\end{array}\right]=\left[\begin{array}{c}3\\5\end{array}\right][/tex]∴ S' is (3 , 5)∵ The point T is (6 , -7)∴ [tex]T'=\left[\begin{array}{cc}0&1\\1&0\end{array}\right]\left[\begin{array}{c}6\\-7\end{array}\right]=[/tex]   [tex]\left[\begin{array}{c}(0)(6)+(1)(-7)\\(1)(6)+(0)(-7)\end{array}\right]=\left[\begin{array}{c}-7\\6\end{array}\right][/tex]∴ T' is (-7 , 6)* Lets look to the figures to find the right answer∵ The R' is (5 , -2) , S' is (3 , 5) , T' is (-7 , 6)∴ The right answer is (d)