Question

true or false: on a number line, if $overline{eg}=8$ and the coordinate of e is 3, then a bisector of $overline{eg}$ would always intersect at 7 or - 5. false true

Explanation:

Step1: Find the possible coordinates of G

If $EG = 8$ and the coordinate of $E$ is $3$, then if $G$ is to the right of $E$, the coordinate of $G$ is $3 + 8=11$, and if $G$ is to the left of $E$, the coordinate of $G$ is $3-8=- 5$.

Step2: Calculate the mid - point in both cases

Case 1: When $E = 3$ and $G = 11$, the mid - point of $\overline{EG}$ is $\frac{3 + 11}{2}=\frac{14}{2}=7$.
Case 2: When $E = 3$ and $G=-5$, the mid - point of $\overline{EG}$ is $\frac{3+( - 5)}{2}=\frac{3 - 5}{2}=\frac{-2}{2}=-1$.

Answer:

F. False