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.

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neela | High School Teacher | (Level 3) Valedictorian

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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.

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