Question

applying the perpendicular bisector theorem. what is the length of segment sr? units. r t q. 2x + 8 8x - 4 s

Explanation:

Step1: Apply perpendicular - bisector theorem

Since line $l$ is the perpendicular bisector of $RQ$, by the perpendicular - bisector theorem, $SR = SQ$. So, $2x + 8=8x - 4$.

Step2: Solve the equation for $x$

Subtract $2x$ from both sides: $2x+8 - 2x=8x - 4-2x$, which simplifies to $8 = 6x - 4$. Then add 4 to both sides: $8 + 4=6x-4 + 4$, getting $12 = 6x$. Divide both sides by 6: $\frac{12}{6}=\frac{6x}{6}$, so $x = 2$.

Step3: Find the length of segment SR

Substitute $x = 2$ into the expression for $SR$ (which is $2x + 8$). Then $SR=2\times2 + 8=4 + 8=12$.

Answer:

12