Question

suppose m is the mid - point of (overline{fg}). find the missing measure.(fg = 14a + 1, fm = 14.5)(a=)

Explanation:

Step1: Recall mid - point property

Since $M$ is the mid - point of $\overline{FG}$, then $FG = 2FM$.

Step2: Substitute given values

We know that $FG=14a + 1$ and $FM = 14.5$. Substituting into $FG = 2FM$, we get $14a+1=2\times14.5$.

Step3: Simplify the right - hand side

$2\times14.5 = 29$, so the equation becomes $14a+1 = 29$.

Step4: Isolate the term with $a$

Subtract 1 from both sides: $14a=29 - 1$.
$14a=28$.

Step5: Solve for $a$

Divide both sides by 14: $a=\frac{28}{14}$.
$a = 2$.

Answer:

$2$