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?
(image shows a diagram with points q, l, l, m, m, with ql = 4, ql = 4 + 4 = 8? wait, no, the diagram has q to l as 4, l to l as 4, q to m as 3, and m to m? wait, the diagram: q is at the bottom, l is above q with ql = 4, l is above l with ll = 4. m is on the segment qm (length 3 from q to m), and m is above m? wait, the dilation is with scale factor 2, center q. so qm should be scale factor times qm. since qm is 3, then qm is 32=6? wait, but lets check the diagram. the diagram: q is the bottom point, l is above q (ql=4), l is above l (ll=4, so ql=8). m is on the segment from q to m (length 3 from q to m), and m is on the segment from q to m? wait, the dilation: when you dilate a segment lm with center q and scale factor 2, then qm = scale factor qm. since qm is 3, then qm = 2*3=6. so the question is to find qm given qm=3 and scale factor 2. so the ocr text is as above, with the diagram showing qm=3, and we need to find qm with scale factor 2.

Explanation:

Step1: Identify QM length

From the graph, QM = 3.

Step2: Apply scale factor to QM

Dilation scale factor = 2, so QM' = QM × 2 = 3×2 = 6.

Answer:

6