triangle stv was dilated with the origin as the center of dilation to form △ stv. what is the scale factor…

triangle stv was dilated with the origin as the center of dilation to form △ stv. what is the scale factor of the dilation? 1/3 2/3 3/2 3/1

triangle stv was dilated with the origin as the center of dilation to form △ stv. what is the scale factor of the dilation? 1/3 2/3 3/2 3/1

Answer

Explanation:

Step1: Identify corresponding side lengths

Let's consider the vertical distance from the top - point to the base of the triangles. For $\triangle STV$, assume the vertical distance from $S$ to the line containing $TV$ is $h_1 = 6$ (counting the grid - squares). For $\triangle S'T'V'$, the vertical distance from $S'$ to the line containing $T'V'$ is $h_2 = 4$.

Step2: Calculate the scale factor

The scale factor $k$ of a dilation is given by the ratio of the corresponding side lengths of the image to the pre - image. If we consider the vertical distances as corresponding lengths, then $k=\frac{h_2}{h_1}$. Substituting $h_1 = 6$ and $h_2 = 4$, we get $k=\frac{4}{6}=\frac{2}{3}$.

Answer:

$\frac{2}{3}$