Question

1. a figure and its dilation are shown below. mark thinks the scale factor is 3/2. max thinks the scale factor is 2/3. who is correct and why?

Explanation:

Step1: Recall the formula for scale factor

Scale factor \(k=\frac{\text{length of dilated figure}}{\text{length of original figure}}\)

Step2: Identify the lengths

Original length \(BC = 17\) ft, dilated length \(B'C'=25.5\) ft

Step3: Calculate the scale factor

\(k=\frac{25.5}{17}=\frac{25.5\div8.5}{17\div8.5}=\frac{3}{2}\)

Answer:

Max is incorrect. Mark is correct. The scale factor \(k = \frac{\text{length of dilated figure}}{\text{length of original figure}}=\frac{25.5}{17}=\frac{3}{2}\)