Offset series of points perpendicular to a line with anothe line as a reference dista

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I need to find out how to move/create a series of points which are already on a line perpendicular left or right to intersect with a second line which runs parallel to the first.

The distance between each of the output points does not need to be the same as the original, but the up/down relationship needs to stay in tact.

An example of this is that if I had a grid line running exactly north/south with points evenly spaced along it, I would need the new output points to be exactly east or west of the original line but sitting right on the second line

This may sound pretty complicated the way Im explaining it but maybe the picture attached may make it clearer.

When offsetting I need to be able to specify a maximum offset distance and would like the new points feature class to contain the same information as the original.I would also like to be able to do it on a mass scale

I was thinking along the lines of:Input Feature Point ClassInput Feature Line Class: Bearing reference linesInput Feature Line Class 2: Intersect lines for new pointsOutput Feature Point Class: with original attributes

Please note I have the following software at my disposal:* ArcGIS 10.1* Global Mapper V15* AutoCAD 2014

Any help or guidance would be greatly appreciated

Cheers




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