Question

points w, x, and y are collinear. point x is between w and y, wx = 7z + 10, xy = 6z + 1, and wy = 15z − 23. find wy.

Explanation:

Step1: Use segment addition postulate

Since \( X \) is between \( W \) and \( Y \), we have \( WX + XY = WY \). Substituting the given expressions, we get \((7z + 10)+(6z + 1)=15z - 23\).

Step2: Simplify the left - hand side

Combine like terms: \(7z+6z + 10 + 1=15z - 23\), which simplifies to \(13z+11 = 15z - 23\).

Step3: Solve for \( z \)

Subtract \(13z\) from both sides: \(11=15z - 13z-23\), so \(11 = 2z-23\). Then add 23 to both sides: \(11 + 23=2z\), \(34 = 2z\). Divide both sides by 2: \(z = 17\).

Step4: Find \( WY \)

Substitute \( z = 17\) into the expression for \( WY \): \(WY=15z - 23=15\times17-23\). Calculate \(15\times17 = 255\), then \(255-23 = 127\).

Answer:

127