Question

1. if line n bisects $overline{qr}$, find $overline{qp}$. 3x + 5 5x - 19 q p r

Explanation:

Step1: Set up the equation

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

Step2: Solve for $x$

Subtract $3x$ from both sides: $3x + 5-3x=5x - 19-3x$, which simplifies to $5 = 2x-19$. Then add 19 to both sides: $5 + 19=2x-19 + 19$, getting $24 = 2x$. Divide both sides by 2: $\frac{24}{2}=\frac{2x}{2}$, so $x = 12$.

Step3: Find the length of $\overline{QP}$

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

Answer:

$41$