Question

in the similarity transformation of \\( \triangle abc \\) to \\( \triangle dfe \\), \\( \triangle abc \\) was dilated by a scale factor of \\( 1 / 2 \\), reflected across the \\( x \\)-axis, and moved through the translation ?.

Explanation:

Step1: Find coordinates of \(B\)

From the graph, \(B=(0, - 2)\)

Step2: Apply dilation and reflection

After dilation by scale factor \(\frac{1}{2}\), \(B\) becomes \((0\times\frac{1}{2},-2\times\frac{1}{2})=(0, - 1)\). After reflection across \(x -\)axis, \(y -\)coordinate changes sign. So the point is \((0,1)\)

Step3: Find translation

The corresponding point \(F\) in \(\triangle DFE\) is \((2,1)\). To get from \((0,1)\) to \((2,1)\), we use the translation \((x + 2,y+0)\)

Answer:

\((x + 2,y-1)\)