Perpendicular on a line from a given point

Question

How can I draw a perpendicular on a line segment from a given point? My line segment is defined as (x1, y1), (x2, y2), If I draw a perpendicular from a point (x3,y3) and it

Answer 1

This is a C# implementation of the accepted answer. It's also using ArcGis to return a MapPoint as that's what we're using for this project.

        private MapPoint GenerateLinePoint(double startPointX, double startPointY, double endPointX, double endPointY, double pointX, double pointY)
        {
            double k = ((endPointY - startPointY) * (pointX - startPointX) - (endPointX - startPointX) * (pointY - startPointY)) / (Math.Pow(endPointY - startPointY, 2) 
                + Math.Pow(endPointX - startPointX, 2));
            double resultX = pointX - k * (endPointY - startPointY);
            double resultY = pointY + k * (endPointX - startPointX);

            return new MapPoint(resultX, resultY, 0, SpatialReferences.Wgs84);
        }

Thanks to Ray as this worked perfectly for me. c#arcgis

Answer 2

Mathematica introduced the function RegionNearest[] in version 10, 2014. This function could be used to return an answer to this question:

{x4,y4} = RegionNearest[Line[{{x1,y1},{x2,y2}}],{x3,y3}]