Question

midpoint: the midpoint of a segment is the point that divides the segment into 2 congruent segments (equal length). m is the midpoint of ab. so am ≅ mb # am = mb. find mq. pm ≅ mq. m is a midpoint of pq. pq = 4 4/5. open - ended question what is the length of mq? type your answer here a 00 rewatch next question

Explanation:

Step1: Recall mid - point property

If $M$ is the mid - point of segment $\overline{PQ}$, then $PM = MQ$ and $PQ=PM + MQ$.

Step2: Given $PQ = 4\frac{4}{7}$

Let $PM = MQ=x$. Then $PQ=x + x=2x$.
We know $PQ = 4\frac{4}{7}=\frac{4\times7 + 4}{7}=\frac{32}{7}$.
Since $2x=\frac{32}{7}$, we solve for $x$.

Step3: Solve for $x$ (length of $MQ$)

Dividing both sides of the equation $2x=\frac{32}{7}$ by 2 gives $x=\frac{1}{2}\times\frac{32}{7}=\frac{16}{7}=2\frac{2}{7}$.

Answer:

$2\frac{2}{7}$