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 dilation property

In dilation, $QM' = 2\times QM$.

Step2: Use Pythagorean theorem

In right - triangle formed by segments from $Q$ to $M$, if we assume the vertical and horizontal distances from $Q$ to $M$ are known. Here, using the given lengths, by Pythagorean theorem $QM=\sqrt{3^{2}+4^{2}}$.

Step3: Calculate length

$QM=\sqrt{9 + 16}=\sqrt{25}=5$.

Answer:

5