Question

line wy is dilated to create line wy using point q as the center of dilation.
what is the scale factor?
given that qy = 4.125, what is qy?

Explanation:

Step1: Calculate scale factor

The scale factor $k$ is the ratio of the length from the center of dilation to the image point to the length from the center to the original point. For points $W$ and $W'$:
$k = \frac{QW'}{QW} = \frac{2 + 3.5}{2} = \frac{5.5}{2} = 2.75$

Step2: Find QY using scale factor

Since dilation scales all distances from the center by $k$, $QY' = k \times QY$. Rearrange to solve for $QY$:
$QY = \frac{QY'}{k} = \frac{4.125}{2.75} = 1.5$

Answer:

Scale factor: $2.75$
$QY$: $1.5$