Final answer:
The coordinate of the fourth vertex D in a square ABCD with known vertices A(-5, 4), B(3, 4), C(3, -4) is D(-5, -4), found by ensuring the square's opposite sides are parallel and equal in length.
Step-by-step explanation:
If we have a square ABCD with three known vertices and we're tasked with finding the coordinates of the fourth vertex D, we need to consider the properties of a square. In a square, opposite sides are parallel and equal in length. Given vertices A(-5,4), B(3,4), and C(3,-4), we can infer that to maintain the properties of a square, vertex D must have the same y-coordinate as vertex A and the same x-coordinate as vertex C.
Vertex A has a y-coordinate of 4, and vertex C has an x-coordinate of 3. So, the fourth vertex D must have an x-coordinate of -5 (the same as A’s x-coordinate because AD will be parallel to BC) and a y-coordinate of -4 (the same as C’s y-coordinate because DC will be parallel to AB). Hence, the coordinate of the fourth vertex D is D(-5, -4).