Question

using scale factors to find missing lengths
line segment lm is dilated to create lm using point q
as the center of dilation and a scale factor of 2.
what is the length of segment qm?

Explanation:

Step1: Recall the formula for dilation

When a segment is dilated with a scale factor \(k\) and center \(Q\), if the original segment has length \(x\) (from the center \(Q\)), the length of the dilated segment \(x'\) is given by \(x'=k\times x\).

Step2: Identify the original length and scale factor

The original length \(QM = 3\), and the scale factor \(k = 2\).

Step3: Calculate the length of \(QM'\)

Using the formula \(QM'=k\times QM\), substitute \(k = 2\) and \(QM=3\). So \(QM'=2\times3 = 6\).

Answer:

\(6\)