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 { a b } \\) is 2.20 units, the length of \\( \overline { l m } \\) is \\( \square \\) units. write your answer as a decimal number to two decimal places.

Explanation:

Step1: Properties of reflection

Reflection is a rigid transformation. So, the length of \(A'B'\) is equal to the length of \(AB\). Since \(AB = 2.20\) units, then \(A'B'=2.20\) units.

Step2: Properties of dilation

Dilation is a similarity transformation. If the scale factor \(k = 0.5\) and the original length is \(l_{original}\) (here \(l_{original}=A'B'\)), and the new - length is \(l_{new}\) (here \(l_{new}=LM\)). The formula for dilation is \(l_{new}=k\times l_{original}\).
Substitute \(k = 0.5\) and \(l_{original}=2.20\) into the formula: \(LM=0.5\times2.20\).
Calculate \(0.5\times2.20=\frac{1}{2}\times2.20 = 1.10\).

Answer:

\(1.10\)