BD is the perpendicular bisector of AC. What is the length of AB and BC?

Question

BD is the perpendicular bisector of AC. What is the length of AB and BC?

  

Answer 1

If a point is on a perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.

B is on the perpendicular bisector, so AB = BC.

Thus 4x - 1 = 1 + 2x

x = 1

Substituting x = 1 back into the equations for AB and BC, they are both equal to 3.

Answer 2

since bd is a perpendicular bisector the two triangles formed are congruent so AB=BC

4X-1=1+2x so x=1 and both sides are 3