Question

1. if r is the mid - point of qs, find qs.

q
5x - 3
r
21 - x
s

Explanation:

Step1: Set up the equation

Since $R$ is the mid - point of $\overline{QS}$, then $QR = RS$. So we set up the equation $5x - 3=21 - x$.

Step2: Solve for $x$

Add $x$ to both sides: $5x+x - 3=21 - x+x$, which simplifies to $6x - 3=21$. Then add 3 to both sides: $6x-3 + 3=21 + 3$, getting $6x=24$. Divide both sides by 6: $\frac{6x}{6}=\frac{24}{6}$, so $x = 4$.

Step3: Find $QR$ or $RS$

Substitute $x = 4$ into the expression for $QR$ (we could also use the expression for $RS$). $QR=5x - 3=5\times4-3=20 - 3=17$.

Step4: Find $QS$

Since $QS=QR + RS$ and $QR = RS$, then $QS = 2\times QR$. So $QS=2\times17 = 34$.

Answer:

34