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Polygon ABCDE is reflected across the x-axis to form polygon A'B'C'DE. Then polygon A'B'C'DE 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 AB is 2.20 units, the length of LM is _______ units.

Write your answer as a decimal number to two decimal places.



Answer :

GinnyAnswer
Sure! Let's break down the steps to solve this problem.

1. Identify the given information:
- The length of segment AB is provided as 2.20 units.
- Polygon ABCDE undergoes a reflection across the x-axis, which does not change the lengths of any of its sides.
- The reflected polygon A'B'C'DE is then dilated by a scale factor of 0.5 about point D.

2. Understand the transformation:
- When a polygon is dilated with a scale factor, the lengths of all its sides are multiplied by that scale factor.
- Thus, under a scale factor of 0.5, each side will become half of its original length.

3. Calculate the length of LM:
- Since vertices A and B correspond to L and M, respectively, the length of segment AB will be dilated to form the length of segment LM.
- To find the new length, multiply the original length of AB by the scale factor of 0.5.

[tex]\[ \text{Length of } LM = \text{Length of } AB \times \text{Scale Factor} \][/tex]

[tex]\[ \text{Length of } LM = 2.20 \text{ units} \times 0.5 \][/tex]

[tex]\[ \text{Length of } LM = 1.10 \text{ units} \][/tex]

Thus, the length of segment LM is 1.10 units.

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