Question

find the measure of (overline{fg}).
diagram: a line segment with points f, g, h, j, k (in order) and tick marks indicating equal segments. the total length from f to k is labeled 16.8 cm.

Explanation:

Step1: Determine the number of segments

From the diagram, we can see that the segment \( \overline{FK} \) is divided into 4 equal - length segments (since there are 4 intervals between the 5 points \( F, G, H, J, K \)). Let the length of each segment (e.g., \( \overline{FG},\overline{GH},\overline{HJ},\overline{JK} \)) be \( x \). The total length of \( \overline{FK} \) is \( 16.8 \) cm, and the length of \( \overline{FK} \) can also be expressed as the sum of 4 equal segments, so \( 4x=16.8 \).

Step2: Solve for \( x \) (length of \( \overline{FG} \))

To find \( x \), we divide both sides of the equation \( 4x = 16.8 \) by 4. Using the formula \( x=\frac{16.8}{4} \), we calculate \( \frac{16.8}{4}=4.2 \).

Answer:

The measure of \( \overline{FG} \) is \( 4.2 \) cm.