1. **Problem statement:** Given rectangle UVWX with diagonals intersecting at point Y, and WY = 16, find VX. 2. **Important property:** In a rectangle, the diagonals are equal in length and bisect each other. This means Y is the midpoint of both diagonals WX and UV. 3. Since Y is the midpoint of diagonal WX, WY = YX. Given WY = 16, then WX = WY + YX = 16 + 16 = 32. 4. Because UVWX is a rectangle, the diagonals WX and UV are equal in length. Therefore, UV = WX = 32. 5. Since VX is a side of the rectangle adjacent to UV, and UVWX is a rectangle, VX equals the length of side WX. 6. The length WX is the same as UV, which is 32, so VX = 32. **Final answer:** $$VX = 32$$