Question

is s the midpoint of $overline{pq}$?
pq = 68, ps = 5x+1, sq =3x-13.

yes, ps=36

yes, sq=ps=34

no, ps=51 and sq=17

Explanation:

Step1: Set up equation for segment lengths

Since $PQ = PS+SQ$ and $PQ = 68$, $PS = 5x + 1$, $SQ=3x - 13$, we have the equation $5x + 1+3x - 13=68$.

Step2: Combine like - terms

Combining like - terms in the left - hand side of the equation gives $8x-12 = 68$.

Step3: Solve for x

Add 12 to both sides: $8x=68 + 12=80$. Then divide both sides by 8, so $x = 10$.

Step4: Find lengths of PS and SQ

Substitute $x = 10$ into the expressions for $PS$ and $SQ$. $PS=5x + 1=5\times10+1=51$, $SQ=3x - 13=3\times10-13 = 17$.

Step5: Determine if S is mid - point

Since $PS
eq SQ$, S is not the mid - point of $\overline{PQ}$.

Answer:

No, PS = 51 and SQ = 17