Question

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

Explanation:

Step1: Use property of line - bisector

Since the line bisects $QR$, we have $QP = PR$. So, $3x + 5=5x - 19$.

Step2: Solve the equation 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 the length of $QP$

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

Answer:

$41$