Question

1. if s is the midpoint of (overline{rt}), (rs = 5x + 17), and (st = 8x - 31), find rs.

Explanation:

Step1: Use the mid - point property

Since \(S\) is the mid - point of \(\overline{RT}\), then \(RS = ST\).
So, \(5x + 17=8x - 31\).

Step2: Solve the equation for \(x\)

Subtract \(5x\) from both sides:
\(5x+17 - 5x=8x - 31-5x\)
\(17 = 3x-31\).
Add \(31\) to both sides:
\(17 + 31=3x-31 + 31\)
\(48 = 3x\).
Divide both sides by \(3\):
\(x=\frac{48}{3}=16\).

Step3: Find the value of \(RS\)

Substitute \(x = 16\) into the expression for \(RS\):
\(RS=5x + 17\).
\(RS=5\times16+17\).
\(RS = 80+17\).
\(RS=97\).

Answer:

\(97\)