Question

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

Explanation:

Step1: Find the length of \(BC\) and \(FE\)

Coordinates of \(B(- 2,0)\) and \(C(-2,-4)\), so \(BC=\vert0 - (-4)\vert = 4\).
Coordinates of \(F(2,1)\) and \(E(2,3)\), so \(FE=\vert3 - 1\vert = 2\).

Step2: Calculate the scale factor

The scale factor \(k=\frac{FE}{BC}\). Substitute \(FE = 2\) and \(BC = 4\) into the formula, \(k=\frac{2}{4}=\frac{1}{2}\).

Answer:

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