Question

preimage image scale factor = \frac{1}{2} 6 22 what is the area of the image? 33 u² 66 u² 12 u² 132 u² before you continue, we recommend completing the day 2 activity, dream design

Explanation:

Step1: Find area of preimage

The preimage is a rectangle with length \(22\) and width \(6\). Area of rectangle is \(length\times width\), so area of preimage is \(22\times6 = 132\) \(u^{2}\).

Step2: Relate scale factor to area scale factor

When a figure is scaled by a scale factor \(k\), the area of the image is \(k^{2}\) times the area of the preimage. Here, scale factor \(k=\frac{1}{2}\), so area scale factor is \((\frac{1}{2})^{2}=\frac{1}{4}\).

Step3: Calculate area of image

Area of image = Area of preimage \(\times\) area scale factor. So, \(132\times\frac{1}{4}=33\) \(u^{2}\).

Answer:

\(33\ u^{2}\) (corresponding to the option "33 \(u^{2}\)")