Question

On a coordinate plane, 2 trapezoids are shown. Trapezoid M O N P has points (negative 5, 4), (negative 2, 5), (negative 2, 2), and (negative 5, 3). Trapezoid C D E F has points (3, negative 5), (4, negative 5), (5, negative 2), (2, negative 2).
Trapezoid CDEF was reflected across the x-axis followed by a 90° rotation about the origin to create the other trapezoid shown on the graph. Which congruency statement applies to the trapezoids?

CDEF ≅ NPOM
CDEF ≅ MNPO
CDEF ≅ NMOP
CDEF ≅ MOPN

Answer 1

Reflect CDEF across the x-axis: C'(3,5), D'(4,5), E'(5,2), F'(2,2).
Rotate those 90° counterclockwise about the origin: (x,y) -> (−y,x).
So the image points are
C'' = (−5,3), D'' = (−5,4), E'' = (−2,5), F'' = (−2,2).

These match the points of trapezoid M O N P, with the correspondence
C → P, D → M, E → O, F → N.
Thus the correct vertex correspondence is
CDEF ≅ PMON.

(That is, C↦P, D↦M, E↦O, F↦N.)