Final answer:
To find the missing coordinate for point Z of rectangle WXYZ, we apply the properties of rectangles with given coordinates W(1,1), X(5,1), and Y(5,4). Z shares its x-coordinate with W and its y-coordinate with Y, so the missing coordinate for Z is Z(1,4).
Step-by-step explanation:
To determine the missing coordinate for point z of rectangle WXYZ, we need to understand the properties of rectangles. A rectangle has four right angles, and opposite sides are equal and parallel. Coordinate geometry principles are applied here for pinpointing the missing point.
Given the coordinates of points W(1,1), X(5,1), and Y(5,4), we can deduce the coordinates of Z. Since WX is a horizontal line segment and WY is a vertical line segment, we can infer that X and Y have the same x-coordinate because they are both on the right side of the rectangle. Similarly, W and Z should have the same x-coordinate since they are on the left side. Since the x-coordinate of W is 1, so will be the x-coordinate of Z.
Also, because W and X have the same y-coordinate, we know that the top and bottom sides of the rectangle are horizontal. Y and Z, therefore, must have the same y-coordinate, which is 4, the y-coordinate of point Y.
Thus, the missing coordinate for point Z is Z(1,4).