Question

Line m is a perpendicular bisector for AB⎯⎯⎯⎯⎯Find x.A) x = 16B) x =10C) x =28D) x =22

Answer 1

Given the triangle shown in the exercise, you know that the line "m" is a Perpendicular Bisector for the side AB of the triangle.

By definition, a Perpendicular Bisector is a line that passes through the midpoint of a segment and forms an angle that measures 90 degrees. Therefore, it divides the segment into two equal parts.

Based on the Perpendicular Bisector Theorem you know that a point on the Perpendicular Bisector of a segment is equidistant from the endpoints of that segment.

Knowing that theorem, you can conclude that, in this case:

`x+6=22`

Then, you can solve for "x":

`\begin{gathered} x=22-6 \\ x=16 \end{gathered}`

Hence, the answer is: Option A.