Question

ch. 5.1 - perpendicular and angle bisectors mix - ass
find the length of \\( \overline { c d } \\) in the figure below.
*** just type the number and nothing else.
\\( c d = \\)

Explanation:

Step1: Use the property of perpendicular bisector

Since \(DB\) is the perpendicular bisector of \(AC\), then \(AD = CD\). So, \(8x - 4=3x + 1\).

Step2: Solve the equation for \(x\)

Subtract \(3x\) from both sides: \(8x-3x - 4=3x-3x + 1\), which simplifies to \(5x-4 = 1\).
Add \(4\) to both sides: \(5x-4 + 4=1 + 4\), so \(5x=5\).
Divide both sides by \(5\): \(x = 1\).

Step3: Find the length of \(CD\)

Substitute \(x = 1\) into the expression for \(CD\) (\(3x + 1\)). Then \(CD=3\times1+1=4\).

Answer:

4