Answer:
Step-by-step explanation:
Based on the given options and the diagonal of the square ABCD, we can determine the coordinates of point D by understanding the properties of a square. In a square, opposite sides are parallel and equal in length, and diagonals bisect each other at a 90-degree angle.
Looking at the diagonal from point A to point C, which goes from (0, 0) to (-6, -6), we can calculate the midpoint of this diagonal to find the center of the square. The midpoint is (-3, -3). Since a square has symmetry, we can then determine the position of point D based on this midpoint. Point D will be symmetric to point A with respect to the center of the square.
Therefore, the coordinates of point D could be: 1. (5, -1) - Not a valid option as it does not reflect symmetry with respect to the center. 2. (0, -6) - Not a valid option as it does not reflect symmetry with respect to the center. 3. (4, -2) - This is a valid option as it reflects symmetry with respect to the center of the square. 4. (-1, -5) - Not a valid option as it does not reflect symmetry with respect to the center. So, based on the properties of a square and the given options, the coordinates of point D could be (4, -2).
