Question

1. using the diagram to the left, if line n bisects qr, find qp.

Explanation:

Step1: Set up the equation for bisection

Since line $n$ bisects $QR$, 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 $QP$

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

Answer:

$41$