Question

practice 5 (from unit 3, lesson 6)
here are squares abcd and efgh.
find a sequence of rigid transformations and dilations that takes square abcd to square efgh.
a translate by the directed line segment ae, which will take b to a point b. then rotate with center e by angle bef. finally, dilate with center e by scale factor 5/2.
b translate by the directed line segment ae, which will take b to a point b. then rotate with center e by angle bef. finally, dilate with center e by scale factor 2/5.
c dilate using center e by scale factor 2/5.
d dilate using center e by scale factor 5/2.

Explanation:

Step1: Analizar la escala

El lado del cuadrado \(ABCD\) es \(5\) y el lado del cuadrado \(EFGH\) es \(2\). La razón de escala \(k\) para una dilatación que transforma \(ABCD\) en \(EFGH\) se calcula como \(k=\frac{lado\ de\ EFGH}{lado\ de\ ABCD}=\frac{2}{5}\).

Step2: Analizar las transformaciones rígidas

Antes de la dilatación, se deben aplicar transformaciones rígidas (traslación y rotación) para alinear los cuadrados. Primero, se traslada el cuadrado \(ABCD\) usando el segmento dirigido \(AE\) (traslación). Luego, se rota el cuadrado trasladado en el ángulo \(B'EF\) (rotación) y finalmente se dilata con centro \(E\) y factor de escala \(\frac{2}{5}\).

Answer:

B. Translate by the directed line segment \(AE\), which will take \(B\) to a point \(B'\). Then rotate with center \(E\) by angle \(B'EF\). Finally, dilate with center \(E\) by scale factor \(\frac{2}{5}\).