Question

in the similarity transformation of \\( \triangle abc \\) to \\( \triangle def \\), \\( \triangle abc \\) was dilated by a scale factor of ?, reflected across the , and moved through the translation .

Explanation:

Step1: Calculate the scale factor

First, find the length of a side in \(\triangle ABC\) and the corresponding side in \(\triangle DEF\).
Let's take \(AC\). The coordinates of \(A(-1,1)\) and \(C(-1,2)\), so \(AC = 2 - 1=1\).
The coordinates of \(D(1,-3)\) and \(F(1,-1)\), so \(DF=\vert-1-(-3)\vert = 2\).
The scale factor \(k=\frac{DF}{AC}\). Since \(DF = 2\) and \(AC = 1\), \(k = 2\).

Answer:

\(2\)