Question

given the pre-image abcd and the image after a dilation, abcd, what is true about the polygons? check all that apply. the length ab is 2. the length ab is 3. the image is smaller than the pre-image. the scale factor is \\(\frac{3}{2}\\). the scale factor is \\(\frac{2}{3}\\).

Explanation:

Step1: Find length of AB

From the graph, A is at (2, -2) and B is at (4, -2). The distance (length) between them is \( |4 - 2| = 2 \). So "The length AB is 2" is true.

Step2: Find length of A'B'

A' is at (2, -3) and B' is at (5, -3). The distance is \( |5 - 2| = 3 \). So "The length A'B' is 3" is true.

Step3: Compare image and pre - image size

The pre - image AB has length 2, the image A'B' has length 3. Since 3>2, the image (A'B'C'D') is larger than the pre - image (ABCD). So "The image is smaller than the pre - image" is false.

Step4: Calculate scale factor

Scale factor \( k=\frac{\text{length of image segment}}{\text{length of pre - image segment}}=\frac{A'B'}{AB}=\frac{3}{2} \). So "The scale factor is \(\frac{3}{2}\)" is true and "The scale factor is \(\frac{2}{3}\)" is false.

Answer:

• The length AB is 2.
• The length A'B' is 3.
• The scale factor is \(\frac{3}{2}\).