Pg 519 (451) - Q10
If line l is perpendicular to and bisects segment AB, then any point
along line l would be the same distance from point A as from point B because
any point along l would be like the vertex of an isosceles triangle with
the 2 other vertices at A and B. The 2 legs
from the point on line l to A and from the point to B would always
be equal in length. Another way to think about it is: at any point
x along line l, you can draw a line from x to A and another from x to B
and make 2 congruent triangles XEA and XEB whose
hypotenuses would be equal. The answer is therefore E, all
points.