line wy is dilated to create line wy using point q as the center of dilation. what is the scale factor…

Explanation:

Step1: Recall scale - factor formula

The scale factor $k$ of a dilation with center $Q$ is given by the ratio of the distance from the center of dilation to a point on the dilated figure to the distance from the center of dilation to the corresponding point on the original figure. For points $W$ and $W'$, $k=\frac{QW'}{QW}$.

Step2: Calculate the scale factor

Given $QW = 2$ and $QW'=3.5$, then $k=\frac{QW'}{QW}=\frac{3.5}{2}=1.75$.

Step3: Use the scale - factor relationship for $Y$ and $Y'$

The relationship between the distances from the center of dilation to corresponding points is $QY'=k\times QY$. We know $k = 1.75$ and $QY'=4.125$. So, $QY=\frac{QY'}{k}$.

Step4: Calculate $QY$

Substitute $k = 1.75$ and $QY'=4.125$ into the formula: $QY=\frac{4.125}{1.75}=\frac{4125}{1750}=\frac{33}{14}=2.35714\approx2.36$ (rounded to two decimal places).

Answer:

Scale factor: $1.75$ $QY$: $2.36$