Question 886087
You can use an altitude that lies on the line AB, since this line will intersect both the midpoint of AB and the vertex at the nonequal sides; because, this triangle is isosceles.  You want the line PERPENDICULAR to line AB and which intersects the midpoint of AB.  A sketch of the graph would help to understand.


MIDPOINT OF SEGMENT AB
{{{x=(4+(-6))/2=-1}}};  {{{y=(10+12)/2=11}}}.


SLOPE OF AB
{{{(12-10)/(-6-4)=-1/5}}}


The line perpendicular must have slope {{{m=5/1=5}}} and contain point (-1,11).


You do NOT want the value of B.  <b>You want the value of b</b> for the line based on {{{y=mx+b}}}.


{{{y-mx=b}}}
{{{b=y-mx}}}
{{{b=11-(5)(-1)}}}
{{{b=11+5}}}
{{{highlight(b=16)}}}