Question

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

I can’t pick the correct letter-for-letter correspondence without seeing the graph or the coordinates of C, D, E, F and M, N, O, P. Can you upload the picture or list the coordinates of the vertices?

Meanwhile, here is the key fact you can use once you have the coordinates:
- Reflecting across the x-axis sends (x,y) → (x,−y).
- Rotating 90° counterclockwise about the origin sends (x,y) → (−y,x).
- The composition (rotate ◦ reflect) sends (x,y) → (y,x). (So each vertex’s coordinates are swapped.)

So to find the matching congruence:
1. Swap the x- and y-coordinates of each original vertex C, D, E, F to get their image points.
2. See which labelled point (M, N, O or P) sits at each swapped coordinate — that gives the vertex correspondence (e.g. C ↦ N, D ↦ M, ...).
3. Write the congruence in the same vertex order around the figure (remember the composition is a reflection, so the orientation is reversed).

Send the diagram or vertex coordinates and I’ll finish it and pick the correct choice.