Question

type the correct answer in the box.
polygon abcde is reflected across the x - axis to form polygon abcde. then polygon abcde is dilated by a scale factor of 0.5 about d to form polygon lmnop. vertices a and b correspond to l and m, respectively.
if the length of \\(\overline{ab}\\) is 2.20 units, the length of \\(\overline{lm}\\) is \\(\boxed{}\\) units. write your answer as a decimal number to two decimal places.
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Explanation:

Step1: Recall reflection property

Reflection across the x - axis is a rigid transformation, so the length of \( \overline{AB} \) and \( \overline{A'B'} \) are equal. So \( AB = A'B'=2.20 \) units.

Step2: Apply dilation scale factor

Dilation with a scale factor \( k = 0.5 \) about a point. The length of a segment after dilation is given by the formula \( \text{New length}=\text{Original length}\times k \). Here, the original length for the segment corresponding to \( LM \) (which is \( A'B' \)) is \( 2.20 \) units and \( k = 0.5 \). So the length of \( \overline{LM}=2.20\times0.5 = 1.10 \) units.

Answer:

\( 1.10 \)