Question

Allison drew a map of where she and her friends live. Allison's house is at point A, and her friends live at points B, C, and D. She only wrote some of the distances, in blocks, on the map. Also, AD¯¯¯¯¯¯¯¯ is a perpendicular bisector of BC¯¯¯¯¯¯¯¯. Allison wants to know the distance between her house and point C.What is the measure of AC?

Answer 1

Solution:

Given that;

Allison drew a map of where she and her friends live.

Allison's house is at point A, and her friends live at points B, C, and D

Where, line segment AD is a perpendicular bisector of BC,

And a perpendicular bisector is a line segment which bisects another line segment at 90 degrees, and divides it into two equal parts..

Since, AD is a perpendicular bisector of BC, then

$\begin{gathered} BD=CD=3 \\ \angle ADB=\angle ADC \\ And,\text{ }AD=CD \\ Thus, \\ \Delta ADB\cong\Delta ADC\text{ \lparen SAS\rparen} \end{gathered}$

Hence,

$AB=AC=4.24$

The measure of AC is 4.24