Question

q is the mid - point of pr. if qr = x + 8 and pr = 4x + 8, what is qr? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use mid - point property

Since $Q$ is the mid - point of $PR$, then $PQ = QR$ and $PR=PQ + QR$. So $PR = 2QR$.

Step2: Set up the equation

We know that $QR=x + 8$ and $PR = 4x+8$. Substituting into $PR = 2QR$, we get $4x + 8=2(x + 8)$.

Step3: Expand the right - hand side

Expand $2(x + 8)$ to $2x+16$. So the equation becomes $4x + 8=2x + 16$.

Step4: Solve for $x$

Subtract $2x$ from both sides: $4x-2x + 8=2x-2x + 16$, which simplifies to $2x+8 = 16$. Then subtract 8 from both sides: $2x+8 - 8=16 - 8$, so $2x=8$. Divide both sides by 2: $x = 4$.

Step5: Find the length of $QR$

Substitute $x = 4$ into the expression for $QR$. Since $QR=x + 8$, then $QR=4 + 8=12$.

Answer:

12