Question

q is the midpoint of pr. what are pq, qr, and pr? 6x - 7 5x + 1

Explanation:

Step1: Set up equation using mid - point property

Since Q is the midpoint of PR, then PQ = QR. So, we set up the equation $6x - 7=5x + 1$.

Step2: Solve for x

Subtract $5x$ from both sides: $6x-5x - 7=5x-5x + 1$, which simplifies to $x-7 = 1$. Then add 7 to both sides: $x=1 + 7$, so $x = 8$.

Step3: Find PQ

Substitute $x = 8$ into the expression for PQ. $PQ=6x - 7=6\times8-7=48 - 7=41$.

Step4: Find QR

Since QR = PQ, $QR = 41$.

Step5: Find PR

$PR=PQ + QR$, so $PR=41+41 = 82$.

Answer:

$PQ = 41$, $QR = 41$, $PR = 82$