Question

q is the midpoint of $overline{pr}$. if $pq = 8x + 1$ and $qr = 7x + 10$, what is $pq?
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 $\overline{PR}$, then $PQ = QR$. So, we set up the equation $8x + 1=7x + 10$.

Step2: Solve for x

Subtract $7x$ from both sides of the equation: $(8x + 1)-7x=(7x + 10)-7x$. This simplifies to $x+1 = 10$. Then subtract 1 from both sides: $x+1 - 1=10 - 1$, so $x = 9$.

Step3: Find the value of PQ

Substitute $x = 9$ into the expression for $PQ$. $PQ=8x + 1$. So, $PQ=8\times9+1$. First, calculate $8\times9 = 72$, then $72+1=73$.

Answer:

73