Question

unit 2 - lesson 5: comprehension check b

1. un rectángulo a se dilata para former el rectángulo a. ¿qué figura muestra el punto que es el centro de dilatación?
2. leila traza las figuras w, x, y, y z, como se muestra.

determina si cada enunciado acerca de las figuras de leila es verdadero.
selecciona verdadero o falso para cada enunciado.

1. dionne traza el triángulo t y su dilatación, el triángulo t, como se muestra.

¿qué factor de escala usó dionne?
a. $\frac{1}{2}$
b. $\frac{1}{3}$
c. $\frac{1}{2}$
d. 2

Explanation:

Step1: Understand the concept of scale factor

The scale factor is the ratio of the length of a side of the dilated figure (\(T'\)) to the length of the corresponding side of the original figure (\(T\)).

Step2: Analyze the triangles

Assume the base of triangle \(T\) is \(1\) unit and the base of triangle \(T'\) is \(\frac{1}{2}\) unit. The scale factor \(k=\frac{\text{side of }T'}{\text{side of }T}\).

Step3: Calculate the scale factor

If we assume the relationship between the sides (by visual inspection of similar - triangle properties in dilation), the scale factor \(k = \frac{1}{2}\) (since the smaller triangle \(T'\) is a dilation of the larger triangle \(T\)). But if we consider the other way (if \(T\) is the dilation of \(T'\)), let the side of \(T'\) be \(x\) and the side of \(T\) be \(2x\). Then the scale factor of \(T'\) with respect to \(T\) is \(k=\frac{x}{2x}=\frac{1}{2}\).

Answer:

B. \(\frac{1}{2}\)