Question

1. point m is the mid - point of $overline{ab}$. find bm.

$a$. 58
$b$. 29
$c$. 133
$d$. 4

Explanation:

Step1: Set up equation using mid - point property

Since $M$ is the mid - point of $\overline{AB}$, then $AM = BM$. So, $4x + 13=3x + 17$.

Step2: Solve for $x$

Subtract $3x$ from both sides: $4x-3x + 13=3x-3x + 17$, which simplifies to $x+13 = 17$. Then subtract 13 from both sides: $x=17 - 13=4$.

Step3: Find $BM$

Substitute $x = 4$ into the expression for $BM$ ($BM=3x + 17$). So, $BM=3\times4+17=12 + 17=29$.

Answer:

b. 29