Question

1. 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 \(QS\), then \(QR = RS\). So, \(5x−3=21 - x\).

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: \(x=\frac{24}{6}=4\).

Step3: Find \(QS\)

\(QS=QR + RS\). Since \(QR = 5x−3\) and \(RS = 21 - x\), and \(x = 4\), then \(QR=5\times4−3=20 - 3 = 17\) and \(RS=21 - 4=17\). So \(QS=17 + 17=34\).

Answer:

34