Question

q is the midpoint of $overline{pr}$. pq = 48 and pr = 3z - 6. find z, qr, and pr.

Explanation:

Step1: Use mid - point property

Since Q is the mid - point of $\overline{PR}$, then $PQ = QR$ and $PR=PQ + QR$. Given $PQ = 48$, so $QR = 48$.

Step2: Set up equation for PR

We know that $PR=3z - 6$ and also $PR=PQ + QR=48 + 48=96$.

Step3: Solve for z

Set $3z-6 = 96$. Add 6 to both sides: $3z=96 + 6=102$. Then divide both sides by 3: $z=\frac{102}{3}=34$.

Answer:

z = 34
QR = 48
PR = 96