Question

q is the midpoint of $overline{pr}$. 8x - 20 9x - 25 p q r find pq, qr, and pr. pq = qr =

Explanation:

Step1: Set up equation using mid - point property

Since Q is the mid - point of $\overline{PR}$, then $PQ = QR$. So, $8x−20=9x - 25$.

Step2: Solve for x

Subtract 8x from both sides: $-20=x - 25$. Then add 25 to both sides, we get $x = 5$.

Step3: Find PQ

Substitute $x = 5$ into the expression for PQ: $PQ=8x−20=8\times5−20=40 - 20=20$.

Step4: Find QR

Since $QR = PQ$, $QR = 20$.

Step5: Find PR

$PR=PQ + QR$, so $PR=20+20 = 40$.

Answer:

PQ = 20, QR = 20, PR = 40