Question

use arrows a and b for problems 3 - 5

1. what is the scale factor from a to b?
2. explain how you know:
3. label each missing side so the lengths of arrow b are proportional to the side lengths of arrow a.

Explanation:

Step1: Identify corresponding sides

Let's consider the horizontal - side lengths. In Arrow A, a horizontal side length is 1 (the small horizontal part on the left), and in Arrow B, the corresponding horizontal side length is 4.

Step2: Calculate scale factor

The scale factor $k$ from Arrow A to Arrow B is found by dividing the length of the corresponding side in Arrow B by the length of the corresponding side in Arrow A. So, $k=\frac{4}{1} = 4$.

Step3: Explain the method

We know the scale factor is 4 because when two figures are similar (proportional), the ratio of corresponding side - lengths is constant. We compared the lengths of corresponding sides of Arrow A and Arrow B.

Step4: Find missing side - lengths for Arrow B

For the vertical part of Arrow A with length 2, the corresponding vertical part in Arrow B will have length $2\times4 = 8$. For the other small horizontal part on the right of Arrow A with length 1, the corresponding part in Arrow B will have length $1\times4 = 4$.

Answer:

1. The scale factor from A to B is 4.
2. We compared the lengths of corresponding sides of Arrow A and Arrow B. The ratio of corresponding side - lengths (e.g., a side of length 1 in A corresponds to a side of length 4 in B) is 4, so the scale factor is 4.
3. For the vertical part corresponding to the 2 - unit side in Arrow A, label it 8 in Arrow B. For the small horizontal part corresponding to the 1 - unit side in Arrow A on the right, label it 4 in Arrow B.