Question

if r is the mid - point of qs, find qs.
q
5x - 3
r
21 - x
s

Explanation:

Step1: Use mid - point property

Since R is the mid - point of QS, we have QR = RS. So, 5x−3=21 - x.

Step2: Solve the equation 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, giving 6x=24. Divide both sides by 6: $\frac{6x}{6}=\frac{24}{6}$, so x = 4.

Step3: Find the length of QS

QS=QR + RS. Substitute x = 4 into the expressions for QR and RS. QR=5x−3=5(4)−3=20 - 3=17, RS=21 - x=21 - 4 = 17. Then QS=17+17=34.

Answer:

34