Question

b. what is the scale factor larissa used to dilate her sketch? explain how you know.

Explanation:

Step1: Recall scale - factor formula

The scale factor \(k\) of a dilation is given by the ratio of the length of a corresponding side in the dilated figure to the length of the corresponding side in the original figure. If the length of a side in the original figure is \(AB\) and the length of the corresponding side in the dilated figure is \(A'B'\), then \(k=\frac{A'B'}{AB}\).

Step2: Identify lengths

We need to measure or be given the lengths of the corresponding sides in the original sketch and the dilated sketch. Let the length of the side in the original sketch be \(l_1\) and the length of the corresponding side in the dilated sketch be \(l_2\). Then the scale - factor \(k = \frac{l_2}{l_1}\).

Step3: Explain determination

If \(k> 1\), the sketch is an enlargement. If \(0

Answer:

The scale factor \(k=\frac{\text{length of corresponding side in dilated sketch}}{\text{length of corresponding side in original sketch}}\). We determine it by measuring or being given the lengths of corresponding sides in the two sketches.