Question

polygon abcdefgh will be dilated by a scale factor of 3.4 with the origin as the center of dilation to produce polygon abcdefgh. what will the length of ah be?
a. 1.7 units
b. 2 units
c. 3.4 units
d. 6.8 units

Explanation:

Step1: Determine original length of \( AH \)

From the graph, \( AH \) is a vertical segment. By counting grid units (or observing coordinates), the length of \( AH \) is 2 units (since it spans from \( y = 4 \) to \( y = 6 \), difference is \( 6 - 4 = 2 \)).

Step2: Apply dilation scale factor

Dilation scales lengths by the scale factor. The scale factor is \( 3.4 \), so the new length \( A'H' = \text{original length} \times \text{scale factor} \).
Substitute: \( A'H' = 2 \times 3.4 = 6.8 \) units.

Answer:

D. 6.8 units