Question

in the figure below, line segment \\( \overline { a c } \\) is a bisector of line segment \\( \overline { d b } \\). \\( \overline { a c } = 14 \\) feet and \\( \overline { d b } = 10 \\) feet. what is the length, in feet, of \\( \overline { e b } \\)?

a 5
b 6
c 7
d 8

Explanation:

Step1: Recall the definition of a bisector

A bisector divides a line segment into two equal parts. So, if $\overline{AC}$ bisects $\overline{DB}$, then $DE = EB$.

Step2: Use the formula for the length of a bisected segment

Since $DB=DE + EB$ and $DE = EB$, we have $DB = 2EB$. Given $DB = 10$ feet, then $EB=\frac{DB}{2}$.
Substitute $DB = 10$ into the formula: $EB=\frac{10}{2}=5$ feet.

Answer:

A. 5