Question

select the correct answer from each drop - down menu.

pqrs and efgh are polygons that can be mapped onto each other using similarity transformations. the transformation that maps polygon pqrs onto polygon efgh is a followed by dilation with a scale factor of

Explanation:

Step1: Analyze the orientation and position

First, observe the orientation of the polygons. Polygon \(EFGH\) is to the right of \(PQRS\). A translation (shifting) is not sufficient as the orientation (in terms of the relative position of vertices) also changes. A rotation is needed to align the orientation.

Step2: Calculate the scale factor

Count the length of a corresponding side. For example, if we consider the vertical side of \(PQRS\) (say \(PQ\): from \(y = 8\) to \(y=12\), length \(l_{PQ}=4\)) and the vertical side of \(EFGH\) (say \(EH\): from \(y = 6\) to \(y = 10\), length \(l_{EH} = 2\)). The scale factor \(k=\frac{l_{EH}}{l_{PQ}}=\frac{2}{4}=\frac{1}{2}\)

Answer:

The transformation that maps polygon \(PQRS\) onto polygon \(EFGH\) is a rotation followed by dilation with a scale factor of \(\frac{1}{2}\)