Question

suppose m is the mid - point of $overline{fg}$. find the missing measure.
$fm = 8a + 1$, $fg = 42$
$a=$

Explanation:

Step1: Recall mid - point property

Since $M$ is the mid - point of $\overline{FG}$, then $FM=\frac{1}{2}FG$.

Step2: Substitute given values

We know that $FM = 8a + 1$ and $FG=42$. Substituting into $FM=\frac{1}{2}FG$, we get $8a + 1=\frac{42}{2}$.

Step3: Simplify the right - hand side

$\frac{42}{2}=21$, so the equation becomes $8a + 1 = 21$.

Step4: Solve for $a$

Subtract 1 from both sides: $8a=21 - 1$, so $8a=20$. Then divide both sides by 8: $a=\frac{20}{8}=\frac{5}{2}=2.5$.

Answer:

$2.5$