Final answer:
The fourth vertex of a rectangle with given vertices is found by matching the x-coordinate of one pair of opposite vertices and the y-coordinate of the other pair. The fourth vertex is (z,v).
Step-by-step explanation:
To find the fourth vertex of a rectangle with given vertices (w,v), (w,z), and (z,z), we need to understand the properties of a rectangle. A rectangle is a quadrilateral with opposite sides that are equal in length and all angles are right angles. Given the coordinates of the three vertices, we can determine that one pair of opposite sides are vertical lines (w coordinate is the same) and the other pair are horizontal lines (z coordinate is the same).
Since we have one vertex at (w,v) and another at (w,z), these two vertices share the same x-coordinate, which means they are vertically aligned. Consequently, the missing vertex must also be vertically aligned with the third given vertex at (z,z). Therefore, the missing vertex will have the same x-coordinate as the (z,z) vertex, which is z.
Next, we need to match the y-coordinate of the missing vertex with that of the (w,v) vertex since they are supposed to be horizontally aligned in the rectangle. As a result, the y-coordinate of the fourth vertex will be v.
The fourth vertex of the rectangle is thus (z, v).