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 dilation formula

The formula for dilation is \( QX'=k\times QX\), where \(k\) is the scale factor, \(QX\) is the original segment length from the center of dilation \(Q\) to a point \(X\), and \(QX'\) is the dilated segment length from \(Q\) to \(X'\). Here, \(k = 2\) and \(QM=3\).

Step2: Calculate \(QM'\)

Substitute \(k = 2\) and \(QM = 3\) into the formula \(QM'=k\times QM\). So, \(QM'=2\times3\).

Answer:

\(6\)