Question

1. if line n bisects $overline{qr}$, find $overline{qp}$.

$q$ $3x + 5$ $p$ $5x - 19$ $r$

Explanation:

Step1: Use the property of a bisector

Since line $n$ bisects $\overline{QR}$, we have $QP = PR$. So, $3x + 5=5x - 19$.

Step2: Solve the equation for $x$

Subtract $3x$ from both sides: $5 = 2x-19$. Then add 19 to both sides: $24 = 2x$. Divide both sides by 2, we get $x = 12$.

Step3: Find the length of $QP$

Substitute $x = 12$ into the expression for $QP$ which is $3x + 5$. So, $QP=3\times12 + 5=36 + 5=41$.

Answer:

$41$