Question

st bisects pr at point q. pr = 4n + 46 and pq = 4n + 15. find qr.

Explanation:

Step1: Recall the definition of bisect

If a line bisects a line - segment, it divides the line - segment into two equal parts. So, $PQ = QR$ and $PR=PQ + QR$. Since $PQ = QR$, we can also write $PR = 2PQ$.

Step2: Substitute the given expressions

We are given that $PR = 4n+46$ and $PQ = 4n + 15$. Substituting into $PR = 2PQ$, we get $4n+46=2(4n + 15)$.

Step3: Expand the right - hand side

$4n+46=8n + 30$.

Step4: Solve for $n$

Subtract $4n$ from both sides: $46=4n + 30$. Then subtract 30 from both sides: $4n=46 - 30=16$. Divide both sides by 4, so $n = 4$.

Step5: Find $QR$

Since $QR = PQ$ and $PQ=4n + 15$, substitute $n = 4$ into the expression for $PQ$. $PQ=4\times4+15=16 + 15=31$. So, $QR = 31$.

Answer:

31