Question

1. if r is the midpoint of $overline{qs}$, find qs.

q 5x - 3 r 21 - x s

Explanation:

Step1: Set up equation using mid - point property

Since \(R\) is the mid - point of \(QS\), then \(QR = RS\). 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: \(6x−3 + 3=21 + 3\), getting \(6x=24\). Divide both sides by 6: \(x=\frac{24}{6}=4\).

Step3: Find \(QR\) and \(RS\)

Substitute \(x = 4\) into the expression for \(QR\): \(QR=5x−3=5\times4−3=20 - 3 = 17\). Substitute \(x = 4\) into the expression for \(RS\): \(RS=21 - x=21 - 4 = 17\).

Step4: Calculate \(QS\)

Since \(QS=QR + RS\), and \(QR = RS = 17\), then \(QS=17+17 = 34\).

Answer:

34