Final answer:
To find the coordinates of the vertices of rectangle WXYZ, information about the position of one vertex and the sides' lengths or other rectangle properties is necessary, but for a scenario using point displacement, one can find the displacement vector by subtracting the coordinates of the initial point from the coordinates of the final point.
Step-by-step explanation:
To determine the coordinates of the vertices of a rectangle in a Cartesian coordinate system, you would need to know at least the coordinates of one vertex and the lengths of the rectangle's sides or some other characteristics such as the orientation and dimensions. However, the provided information about displacement in three-dimensional space can be applied in a similar manner to find the displacement between two points in the Cartesian coordinate system. The displacement vector Ā from point b to point e can be found using the formula for the scalar components Dx and Dy, where:
(Dx, Dy) = (x2 − x1, y2 − y1).
Substituting the given points b(6.0, 1.6) and e(2.0, 4.5) into this equation would yield:
(Dx, Dy) = (2.0 − 6.0, 4.5 − 1.6), which simplifies to (Dx, Dy) = (-4.0, 2.9). To express this in vector component form, we use:
Ā = Di + Dj, which results in Ā = -4.0i + 2.9j.