Question

in the diagram, the length of segment bc is 23 units. what is the length of segment dc? 13 units 18 units 33 units 46 units

Explanation:

Step1: Use the property of perpendicular bisector

Since \(DB\) is the perpendicular bisector of \(AC\), we have \(AD = DC\) and \(AB=BC\). Given \(BC = 23\) units, and \(AB=2x + 7\), so \(2x+7=23\).

Step2: Solve the equation for \(x\)

Subtract \(7\) from both sides of \(2x + 7=23\):
\(2x=23 - 7\)
\(2x=16\)
Divide both sides by \(2\): \(x = 8\)

Step3: Find the length of \(AD\)

Substitute \(x = 8\) into \(AD=4x + 1\):
\(AD=4\times8+1=32 + 1=33\)

Step4: Determine the length of \(DC\)

Since \(AD = DC\) (by the property of perpendicular bisector), \(DC = 33\) units

Answer:

33 units