Question

suppose m is the mid - point of fg. use the given information to find the missing measure of value. 19. fm = 3x - 4, mg = 5x - 26, fg =?

Explanation:

Step1: Recall mid - point property

Since $M$ is the mid - point of $\overline{FG}$, then $FM = MG$.
So, $3x−4 = 5x−26$.

Step2: Solve for $x$

Subtract $3x$ from both sides:
$3x−4−3x=5x−26−3x$
$- 4 = 2x−26$.
Add 26 to both sides:
$-4 + 26=2x−26 + 26$
$22 = 2x$.
Divide both sides by 2:
$\frac{22}{2}=\frac{2x}{2}$
$x = 11$.

Step3: Find $FG$

Since $FG=FM + MG$ and $FM = MG$, we can use either $FM$ or $MG$ to find $FG$.
First, find $FM$ when $x = 11$: $FM=3x−4=3\times11−4=33 - 4=29$.
Then $FG = 2FM$ (because $FM = MG$).
So $FG=2\times29 = 58$.

Answer:

$58$