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 \\(\underline{}\\) units. write your answer as a decimal number to two decimal places.

Explanation:

Step1: Recall reflection property

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

Step2: Apply dilation formula

Dilation with a scale factor \(k\) about a point changes the length of a segment by the scale factor. The scale factor here is \(k = 0.5\). The length of \(\overline{LM}\) (which is the image of \(\overline{A'B'}\) after dilation) is given by \(LM=k\times A'B'\).
Substitute \(k = 0.5\) and \(A'B'=2.20\) into the formula: \(LM = 0.5\times2.20\)
\(LM=1.10\)

Answer:

1.10