in the diagram, the length of segment bc is 23 units. what is the length of segment dc? 13 units 18 units 33…
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
Answer
Explanation:
Step1: Set up an equation using congruent - side properties
Since the perpendicular bisector (l) of (AC) implies (AB = BC). We set (2x + 7=23). [2x+7 = 23]
Step2: Solve the equation for (x)
Subtract 7 from both sides: (2x=23 - 7=16). Then divide both sides by 2, so (x = 8). [x=\frac{16}{2}=8]
Step3: Find the length of (AD)
Substitute (x = 8) into the expression for (AD): (AD=4x + 1=4\times8+1=32 + 1=33). [AD=4\times8 + 1=33]
Step4: Use the property of the perpendicular bisector
Since (l) is the perpendicular bisector of (AC), (AD = DC). So (DC = 33) units.
Answer:
33 units