What is the locus of points in space that are equidistant from two parallel planes?Describe in words the locus that satisfies the given condition.

Let AB and CD be 2 || line segments in space, so that ABCD
is quadrilateral. ( A, B, C and  are coplanar
points.)

Complete the quadrilateral
ABCD.

Let X be the mid point od AD  and Y be mid point of
BC.

Then XY is also a || line between the || lines keeping
equal distance  from AB and CD in the plane of ABCD.

Let L
be a perpendicular plane to the plane ABCD through the line
XY.

Now all the points on the plane L are equidistant from
the || lines AB and CD.

So the locus of the
points in space that are equidistant from two parallel lines is a plane perpendicular to
the plane of the || lines. This plane passes through all the midpoints between the two
|| lines.