Final answer:
The correct transformation to produce the given coordinates A'(4,5), B'(-6,4), C'(-7, -3), and D' (5,-4) is a rotation of 90 degrees followed by a reflection about the x-axis.
Step-by-step explanation:
In order to transform the given coordinates A'(4,5), B'(-6,4), C'(-7, -3), and D' (5,-4), the correct transformation is a rotation of 90 degrees followed by a reflection about the x-axis. To perform a rotation of 90 degrees counterclockwise, we swap the x and y coordinates of each point and negate the new x-coordinate. So, A' becomes A''(5, -4), B' becomes B''(4, 6), C' becomes C''(-3, 7), and D' becomes D''(-4, 5). Then, to reflect the points about the x-axis, we negate the y-coordinate of each point. Therefore, A'' becomes A'(5, 4), B'' becomes B'(-6, -4), C'' becomes C'(-7, 3), and D'' becomes D'(5, -4).