Final answer:
The question involves translating coordinates by applying a translation vector (h+3, k-5) to each point's coordinates, by adding 3 to the x-coordinate and subtracting 5 from the y-coordinate.
Step-by-step explanation:
The student question involves translating the coordinates by moving every point a certain distance in the horizontal and vertical directions, specified by the translation vector (h+3, k-5). To find the new coordinates of points D', E', F', and G', we will apply this translation to the initial coordinates of these points. To do this, add 3 to the x-coordinate (horizontal movement to the right) and subtract 5 from the y-coordinate (vertical movement downward) of each point's coordinates.
For example, if point D initially has coordinates (xd, yd), the new coordinates after the translation will be (xd+3, yd-5). It's important to apply the same rule consistently to all given points. This process corresponds to a basic concept in coordinate geometry known as coordinate translation.