Question

1. points x, y, and z are collinear. point y bisects xz. find xz if xy = 2x - 4; yz = x + 12. xz =

Explanation:

Step1: Use the definition of a bisector

Since Y bisects XZ, \( XY = YZ \). So we set up the equation \( 2x - 4 = x + 12 \).

Step2: Solve for x

Subtract x from both sides: \( 2x - x - 4 = x - x + 12 \), which simplifies to \( x - 4 = 12 \). Then add 4 to both sides: \( x - 4 + 4 = 12 + 4 \), so \( x = 16 \).

Step3: Find the length of XY and YZ

First, find \( XY \): substitute \( x = 16 \) into \( XY = 2x - 4 \), so \( XY = 2(16) - 4 = 32 - 4 = 28 \). Then find \( YZ \): substitute \( x = 16 \) into \( YZ = x + 12 \), so \( YZ = 16 + 12 = 28 \).

Step4: Find XZ

Since \( XZ = XY + YZ \), and \( XY = YZ = 28 \), then \( XZ = 28 + 28 = 56 \).

Answer:

\( 56 \)