To determine whether or not the polygons are congruent, let's first plot the quadrilaterals WXYZ and CDEF using the given coordinates.
Two congruent figures have the same shape and size. We can check that by using congruence transformations to map one polygon onto the other. In our case, both polygons are trapezoids. If we rotate trapezoid WXYZ 90^(∘) about the origin, the figures will have the same orientation.
To perform the rotation, we can use the coordinate rule. When a figure is rotated 90^(∘) counterclockwise about the origin, the coordinates of the figure's vertices change such that (a,b)→ (- b,a).
(a,b)
(- b ,a)
W(-3,1)
W'(-1,-3)
X(2,1)
X'(-1,2)
Y(4,-4)
Y'(4,4)
Z(-5,-4)
Z'(4,-5)
Notice that the new vertices have the same coordinates as trapezoid CDEF.
We mapped figures onto each other. Therefore, trapezoid CDEF is a 90^(∘) rotation about the origin of trapezoid WXYZ. A rotation is a congruence transformation, so they are congruent.
