Question

1. if t is the midpoint of (overline{su}), find x.

points: ( s ) --- ( 8x + 11 ) --- ( t ) --- ( 12x - 1 ) --- ( u ) (on a straight line)

Explanation:

Step1: Recall midpoint definition

If \( T \) is the midpoint of \( \overline{SU} \), then \( ST = TU \). So we set \( 8x + 11 = 12x - 1 \).

Step2: Solve for \( x \)

Subtract \( 8x \) from both sides: \( 11 = 4x - 1 \).
Add 1 to both sides: \( 12 = 4x \).
Divide by 4: \( x = \frac{12}{4} = 3 \).

Answer:

\( x = 3 \)