Question

pentagon abcde is the image of pentagon abcde under a dilation with a scale factor of \\(\frac{3}{2}\\).

grid with pentagon abcde

what is the length of segment \\(\overline{ae}\\)?

\\(\square\\) units

Explanation:

Step1: Find length of \( A'E' \)

From the grid, count the units for \( A'E' \). Let's assume \( A'E' \) is 6 units (by counting grid squares, since it's a horizontal segment).

Step2: Use dilation scale factor

Dilation scale factor \( k = \frac{3}{2} \). For dilation, \( \text{Image length} = k \times \text{Original length} \). So, \( A'E' = \frac{3}{2} \times AE \).

Step3: Solve for \( AE \)

Rearrange the formula: \( AE = \frac{A'E'}{k} \). Substitute \( A'E' = 6 \) and \( k = \frac{3}{2} \):
\( AE = \frac{6}{\frac{3}{2}} = 6 \times \frac{2}{3} = 4 \).

Answer:

4