Question

q is the midpoint of $overline{pr}$. pq = 34 and pr = 2z - 4. find z, qr, and pr.

Explanation:

Step1: Use mid - point property

Since Q is the mid - point of $\overline{PR}$, then $PQ = QR$ and $PR=2PQ$. Given $PQ = 34$, so $QR = 34$ and $PR=2\times34 = 68$.
Also, we know that $PR = 2z-4$.

Step2: Solve for z

Set up the equation $2z - 4=68$.
Add 4 to both sides: $2z=68 + 4=72$.
Divide both sides by 2: $z=\frac{72}{2}=36$.

Answer:

$z = 36$
$QR = 34$
$PR = 68$