Question

quadrilateral 1 and quadrilateral 2 are polygons that can be mapped onto each other using similarity transformations. the transformation that maps quadrilateral 1 onto quadrilateral 2 is a followed by a dilation with a scale factor of

Explanation:

Step1: Analyze the orientation and position

First, observe the orientation and position of the two quadrilaterals. Quadrilateral 1 needs to be rotated and translated to match the position - like orientation of quadrilateral 2.

Step2: Determine the rotation

By comparing the sides and angles of the two quadrilaterals, we can see that quadrilateral 1 needs to be rotated 180° about the origin to roughly match the orientation of quadrilateral 2.

Step3: Determine the translation

After rotating 180°, we find that quadrilateral 1 also needs to be translated. Counting the grid - units, it needs to be translated down and to the right.

Step4: Determine the dilation factor

To find the dilation factor, we can compare the lengths of corresponding sides. For example, if we take one side of quadrilateral 1 and its corresponding side of quadrilateral 2, and measure their lengths on the grid. Suppose the length of a side of quadrilateral 1 is \(l_1\) and the length of the corresponding side of quadrilateral 2 is \(l_2\). After measurement, we find that the dilation factor \(k=\frac{l_2}{l_1}\). By counting the grid - units of corresponding sides, we find that the dilation factor is \(\frac{1}{2}\).

Answer:

The transformation that maps quadrilateral 1 onto quadrilateral 2 is a 180° rotation about the origin, followed by a translation, and then a dilation with a scale factor of \(\frac{1}{2}\).