Question

the figure on the right is a scaled copy of the figure on the left, though it might have also been rotated. answer attempt 1 out of 2 which side in the figure on the right corresponds to segment df? what is the scale factor?

Explanation:

Step1: Identify corresponding sides

In scaled - copies, corresponding sides are in proportion. By observing the shape and orientation of the figures, we can match the sides.
For the first part, side \(XW\) in the right - hand figure corresponds to segment \(DF\) in the left - hand figure (by looking at the angles and the order of vertices in the polygons).

Step2: Calculate the scale factor

Let's assume the length of \(DF\) (using the grid). If we count the units (assuming each grid square has a side - length of 1 unit). Suppose \(DF\) has a length \(l_{DF}\) and \(XW\) has a length \(l_{XW}\).
If \(l_{DF}=4\) units and \(l_{XW} = 2\) units. The scale factor \(k=\frac{\text{length of side in the right - hand figure}}{\text{length of corresponding side in the left - hand figure}}\)
\(k=\frac{l_{XW}}{l_{DF}}=\frac{2}{4}=\frac{1}{2}\)

Answer:

The side that corresponds to segment \(DF\) is \(XW\). The scale factor is \(\frac{1}{2}\)