Final answer:
The coordinates of point Z in rectangle WXYZ are (6,5).
Step-by-step explanation:
To find the coordinates of point Z in rectangle WXYZ, we can use the fact that opposite sides of a rectangle are parallel and equal in length. Firstly, we find the equation of the line passing through points W and Y using the formula y = mx + b.
Substituting the coordinates of W (3,5) and Y (2,-3), we get y = -4x + 17.
Next, we use the equation of the line to find the coordinates of point Z, which lies on the line containing WY and is equidistant from X and Y.
We substitute the x-coordinate of X (6) into the equation of the line, giving us the y-coordinate of Z, which is 5. Therefore, the coordinates of point Z are (6,5).