Question

pre-image abcd was dilated to produce image abcd. what is the scale factor from the pre-image to the image? enter your answer in the box as a fraction in simplest form.

Explanation:

Step1: Identify corresponding sides

The side of the pre - image (ABCD) is 12 and the corresponding side of the image (A'B'C'D') is 9.

Step2: Calculate scale factor

The scale factor \(k\) from pre - image to image is given by the ratio of the length of the image side to the length of the pre - image side. So \(k=\frac{\text{Length of image side}}{\text{Length of pre - image side}}=\frac{9}{12}\).

Step3: Simplify the fraction

Simplify \(\frac{9}{12}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 3. \(\frac{9\div3}{12\div3}=\frac{3}{4}\).

Answer:

\(\frac{3}{4}\)