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: Set up the equation

Since \(AD = DC\) (by the property of perpendicular bisector), and \(AD=4x + 1\), \(AB = 2x+7\). Also, \(AD = AB\) (by the property of perpendicular bisector). So \(4x+1=2x + 7\).

Step2: Solve for \(x\)

Subtract \(2x\) from both sides: \(4x-2x+1=2x-2x + 7\), which gives \(2x+1=7\). Then subtract \(1\) from both sides: \(2x=7 - 1=6\). Divide by \(2\): \(x = 3\).

Step3: Find \(AD\)

Substitute \(x = 3\) into \(AD=4x + 1\). So \(AD=4\times3+1=13\).

Step4: Find \(DC\)

Since \(AD = DC\) (by the property of perpendicular bisector), \(DC=13\) units.

Answer:

13 units