Question

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

Explanation:

Step1: Recall scale - factor formula

The scale factor \(k\) of a dilation is the ratio of the length of a corresponding side of the dilated figure to the length of the corresponding side of the original figure.

Step2: Select corresponding sides

Let's assume we can find a pair of corresponding sides. For example, if we consider a horizontal or vertical side of the triangles \(\triangle STV\) and \(\triangle S'T'V'\). Suppose the length of a side of the original triangle \(\triangle STV\) is \(a\) and the length of the corresponding side of the dilated triangle \(\triangle S'T'V'\) is \(b\). The scale - factor \(k=\frac{b}{a}\). By counting the grid units for a corresponding side (say a horizontal side), if the length of a side of the original triangle is \(1\) unit and the length of the corresponding side of the dilated triangle is \(3\) units, then \(k = 3\).

Answer:

\(3\)