Question

which composition of transformations would map lmno to lmno?
options (from left to right):

1. ( r_w circ r_{m, 180^circ} )
2. ( r_{m, 180^circ} circ r_{n, 90^circ} )
3. ( r_{m, 90^circ} circ r_{n, 180^circ} )
4. ( r_{m, 180^circ} circ r_w )

(diagram includes blue rectangles lmno, lmno, gray rectangle lmno, and vertical line ( w ) with red arrows.)

Explanation:

Step1: Analyze transformation composition

Identify rotations (R) around points M/N with angles 90°/180° and translations (T). Order: apply second transformation first.

Step2: Match figure orientation/position

Original LMNO to L''M''N''O'' shows 180° rotation around M after 90° rotation around N, aligning with R_M,180°∘R_N,90°.

Answer:

R_M, 180° ∘ R_N, 90°