Question

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

When a point \( M \) is dilated with center \( Q \) and scale factor \( k \), the length of \( QM'=k\times QM \)

Step2: Identify the values

From the figure, \( QM = 3 \) and the scale factor \( k = 2 \)

Step3: Calculate \( QM' \)

Substitute the values into the formula: \( QM'=2\times3=6 \)

Answer:

\( 6 \)