Question

1. choose the best answer. calculate the length of segment $overline{ab}$ with midpoint, $m$, if $overline{am}=5$. 20 10 1 2.5 15) choose the best answer. calculate the length of segment $overline{rs}$ with midpoint, $m$, if $overline{rm}=5x$ and $overline{ms}=x + 12$. 30 36 15 25

Explanation:

Step1: Recall mid - point property

The mid - point of a line segment divides the segment into two equal parts. So if $M$ is the mid - point of $\overline{AB}$, then $AB = 2AM$.

Step2: Calculate length of $\overline{AB}$

Given $AM = 5$, then $AB=2\times5 = 10$.

Step3: For the second problem, use mid - point property

Since $M$ is the mid - point of $\overline{RS}$, then $RM = MS$. So we set up the equation $5x=x + 12$.

Step4: Solve the equation for $x$

Subtract $x$ from both sides: $5x−x=x + 12−x$, which gives $4x=12$. Then divide both sides by 4: $x = 3$.

Step5: Calculate length of $\overline{RS}$

$RS=RM + MS$. Since $RM = 5x$ and $MS=x + 12$, and $x = 3$, then $RM=5\times3 = 15$ and $MS=3 + 12=15$. So $RS=15+15 = 30$.

Answer:

1. B. 10
2. A. 30