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 \(AC\), then \(AD = DC\) and \(AB=BC\). Given \(BC = 23\) units, so \(AB=2x + 7=23\).
Solve the equation \(2x+7 = 23\):
Subtract 7 from both sides: \(2x=23 - 7=16\).
Divide both sides by 2: \(x=\frac{16}{2}=8\).

Step2: Find the length of \(AD\)

Substitute \(x = 8\) into \(AD=4x + 1\).
\(AD=4\times8+1=32 + 1=33\).
Since \(AD = DC\) (by the property of perpendicular bisector), then \(DC = 33\).

Answer:

33 units