Question

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

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

Explanation:

Step1: Set up the equation

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

Step2: Solve for $x$

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

Step3: Find $QP$

Substitute $x = 12$ into the expression for $QP$: $QP=3x + 5=3\times12 + 5=36 + 5=41$.

Answer:

$41$