Answer: (3,-16)
Explanation:
Translation is a geometric transformation that moves every point of a figure, shape or space by the same distance in a given direction. In this case, point D(0,6) is translated to D’(-2,-3) under translation T. To find the image of point (5,-7) under the same translation, we need to apply the same transformation to it.
Let’s first find the vector that connects D to D’. We can do this by subtracting the coordinates of D from the coordinates of D’:
D’ - D = (-2, -3) - (0, 6) = (-2, -9)
This vector represents the distance and direction that we need to move point (5,-7) to get its image under the same translation. To find the image of point (5,-7), we add this vector to its coordinates:
(5,-7) + (-2,-9) = (3,-16)
Therefore, the image of point (5,-7) under the same translation is (3,-16).