Question

r is the midpoint of $overline{qs}$. if $rs = x$ and $qs = 5x - 5$, what is $qs?
simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use mid - point property

Since $R$ is the mid - point of $\overline{QS}$, then $RS=\frac{1}{2}QS$. Given $RS = x$ and $QS = 5x-5$, we have the equation $x=\frac{1}{2}(5x - 5)$.

Step2: Solve the equation for $x$

Multiply both sides of the equation $x=\frac{1}{2}(5x - 5)$ by 2 to get $2x=5x - 5$. Then subtract $2x$ from both sides: $0 = 5x-2x - 5$, which simplifies to $0 = 3x-5$. Add 5 to both sides: $3x=5$, and then $x=\frac{5}{3}$.

Step3: Find the value of $QS$

Substitute $x = \frac{5}{3}$ into the expression for $QS$. $QS=5x - 5=5\times\frac{5}{3}-5=\frac{25}{3}-5=\frac{25}{3}-\frac{15}{3}=\frac{25 - 15}{3}=\frac{10}{3}=3\frac{1}{3}$.

Answer:

$3\frac{1}{3}$