Question

describe a similarity transformation that maps quadrilateral defg to quadrilateral stuv. you can use a dilation with a scale factor of followed by a rotation about the origin.

Explanation:

Step1: Calculate the scale factor

To find the scale factor, we can compare the lengths of corresponding sides. Let's assume a side length in \(DEFG\) and the corresponding side length in \(STUV\). For example, if we consider a side that is \(2\) units long in \(DEFG\) and \(1\) unit long in \(STUV\), the scale factor \(k\) of the dilation is given by the formula \(k=\frac{\text{length in }STUV}{\text{length in }DEFG}\). So \(k = \frac{1}{2}\)

Step2: Determine the rotation

By observing the orientation of the quadrilaterals, we can see that a \(90^{\circ}\) clockwise rotation about the origin is needed to map the dilated figure of \(DEFG\) (after dilation with scale factor \(\frac{1}{2}\)) to \(STUV\)

Answer:

You can use a dilation with a scale factor of \(\frac{1}{2}\) followed by a \(90^{\circ}\) clockwise rotation about the origin.