Question

if r is the mid - point of qs, rs = 2x + 4, and qr = 8x - 38, then what is the measure of each segment?

Explanation:

Step1: Set up the equation

Since $R$ is the mid - point of $QS$, then $QR = RS$. So we set up the equation $8x - 38=2x + 4$.

Step2: Solve for $x$

Subtract $2x$ from both sides: $8x-2x - 38=2x-2x + 4$, which simplifies to $6x-38 = 4$. Then add 38 to both sides: $6x-38 + 38=4 + 38$, getting $6x=42$. Divide both sides by 6: $x=\frac{42}{6}=7$.

Step3: Find the length of $RS$

Substitute $x = 7$ into the expression for $RS$. $RS=2x + 4=2\times7+4=14 + 4=18$.

Step4: Find the length of $QR$

Substitute $x = 7$ into the expression for $QR$. $QR=8x - 38=8\times7-38=56 - 38=18$.

Answer:

$x = 7$
$RS = 18$
$QR = 18$