Question

1.4.7 check your understanding
\\(\overline{fh}\\) is shown with points s, w, and z.

complete the statements.

point is the midpoint of \\(\overline{sz}\\) because it divides segment into two segments of equal length. the scale factor that can be used to dilate to create \\(\overline{wz}\\) is \\(\frac{1}{2}\\)

#f #h #s #w #z #\\(\overline{fh}\\) #\\(\overline{fs}\\) #\\(\overline{fw}\\) #\\(\overline{sz}\\) #\\(\overline{fz}\\)

Explanation:

Step1: Recall mid - point definition

A mid - point divides a line segment into two equal parts. For segment $\overline{SZ}$, point $W$ divides it into two equal segments $\overline{SW}$ and $\overline{WZ}$, so $W$ is the mid - point of $\overline{SZ}$.

Step2: Analyze dilation

If the scale factor of dilation is $\frac{1}{2}$, it means the new segment is half the length of the original segment. To get $\overline{WZ}$ from another segment with a scale factor of $\frac{1}{2}$, we consider $\overline{FZ}$ because $\overline{WZ}$ is half of $\overline{FZ}$ in terms of length relationships on the line $\overline{FH}$.

Answer:

Point $W$ is the midpoint of $\overline{SZ}$ because it divides segment $\overline{SZ}$ into two segments of equal length. The scale factor that can be used to dilate $\overline{FZ}$ to create $\overline{WZ}$ is $\frac{1}{2}$.