Question

1. if line y bisects ac, ab = 4 - 5x, and bc = 2x + 25, find ac.

Explanation:

Step1: Use the property of a bisector

Since line \(y\) bisects \(AC\), then \(AB = BC\). So we set up the equation \(4 - 5x=2x + 25\).

Step2: Solve the equation for \(x\)

Add \(5x\) to both sides: \(4=2x + 25+5x\), which simplifies to \(4 = 7x+25\). Then subtract 25 from both sides: \(4 - 25=7x\), so \(- 21 = 7x\). Divide both sides by 7, we get \(x=-3\).

Step3: Find the length of \(AB\) or \(BC\)

Substitute \(x = - 3\) into the expression for \(AB\): \(AB=4-5\times(-3)=4 + 15=19\).

Step4: Calculate the length of \(AC\)

Since \(AC=AB + BC\) and \(AB = BC\), then \(AC = 2AB\). So \(AC=2\times19 = 38\).

Answer:

38