Question

question 4 (2 points) if r is the mid - point of $overline{qs}$, find qs. $2x + 16$ $5x - 17$ q r s x = qs =

Explanation:

Step1: Set up equation

Since $R$ is the mid - point of $\overline{QS}$, then $QR = RS$. So we set up the equation $2x + 16=5x - 17$.

Step2: Solve for $x$

Subtract $2x$ from both sides: $16 = 5x-2x - 17$, which simplifies to $16 = 3x - 17$. Then add 17 to both sides: $16 + 17=3x$, so $33 = 3x$. Divide both sides by 3: $x=\frac{33}{3}=11$.

Step3: Find $QS$

$QS=QR + RS=(2x + 16)+(5x - 17)$. Substitute $x = 11$ into the expression: $QS=(2\times11 + 16)+(5\times11 - 17)=(22 + 16)+(55 - 17)=38+38 = 76$.

Answer:

$x = 11$
$QS = 76$