Question

1. what is the length of (overline{yz}) when y is the midpoint of (overline{xz})? diagram: line segment ( xyz ) with ( xy = 12 - x ), ( yz = 3x + 4 ) options: ( 2, 10, 16, 20 ) 10) points a and b are plotted on a number line. what is the location of m, the midpoint...

Explanation:

Step1: Set up equation for midpoint

Since \( Y \) is the midpoint of \( \overline{XZ} \), \( XY = YZ \). So \( 12 - x = 3x + 4 \).

Step2: Solve for \( x \)

Add \( x \) to both sides: \( 12 = 4x + 4 \). Subtract 4: \( 8 = 4x \). Divide by 4: \( x = 2 \).

Step3: Find \( XY \) and \( YZ \)

\( XY = 12 - 2 = 10 \), \( YZ = 3(2) + 4 = 10 \).

Step4: Find \( XZ \)

\( XZ = XY + YZ = 10 + 10 = 20 \).

Answer:

20