Question

1. if r is the mid - point of $overline{qs}$, find $qs$.

$2x + 16$ $xlongequal{}$ $5x - 17$

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 $QR$ or $RS$

Substitute $x = 11$ into the expression for $QR$: $QR=2x + 16=2\times11 + 16=22 + 16 = 38$. (We could also use the expression for $RS$).

Step4: Find $QS$

Since $QS=QR + RS$ and $QR = RS$, then $QS = 2\times QR$. So $QS=2\times38 = 76$.

Answer:

76