creating a right angled rectangle on google maps from a line - algorithm

Question

I have an application where the user draws a line, then automatically the software should create a rectangle where the line intersects the midpoint of two adjacent sides of a right angled rectangle. See below, the red line is user drawn and the purple rectangle is calculated. My algorithm almost works, in some directions the rectangles aren't right angled. I want to know why, there is a fair amount of approximation in my code, which should be fine based on the scales I use (a few km). I shouldn't have to worry about the curvature of the earth.
Anybody know how I can improve my code?
Here are my references:
calculate points
lat and long to meters
public static MapRectangle CreatMapRectangle(BalingZone zone, double thickness)
{
MapsCoordinate rectpoint2;
MapsCoordinate rectPoint1 ;
MapsCoordinate rectPoint3 ;
MapsCoordinate rectPoint4 ;
var point1 = zone.Coordinates[0];
var point2 = zone.Coordinates[1];
var latitudeDiff = LatitudeDiffToMeters(point2.Latitude - point1.Latitude);
var longitudeDiff = LongitudeDiffToMeters(point1.Longitude - point2.Longitude, point1.Latitude);
var slopeB = longitudeDiff / latitudeDiff;
double latOffset = thickness * (slopeB / Math.Sqrt(1 + slopeB * slopeB));
double longOffset = thickness * (1 / Math.Sqrt(1 + slopeB * slopeB));
double p3Lat = CalculateLatitude(point1.Latitude, latOffset);
double p3Long = CalculateLongitude( point1.Longitude, p3Lat , longOffset);
rectPoint1 = new MapsCoordinate(p3Lat, p3Long);
double p4Lat = CalculateLatitude(point1.Latitude, -latOffset);
double p4Long = CalculateLongitude(point1.Longitude, p4Lat, -longOffset);
rectpoint2 = new MapsCoordinate(p4Lat, p4Long);
double p5Lat = CalculateLatitude(point2.Latitude, latOffset);
double p5Long = CalculateLongitude( point2.Longitude, p5Lat , longOffset);
rectPoint4 = new MapsCoordinate(p5Lat, p5Long);
double p6Lat = CalculateLatitude(point2.Latitude, -latOffset);
double p6Long = CalculateLongitude( point2.Longitude, p6Lat , -longOffset);
rectPoint3 = new MapsCoordinate(p6Lat, p6Long);
return new MapRectangle(rectPoint4, rectPoint3, rectPoint1, rectpoint2, thickness);
}
//use the quick and dirty estimate that 111,111 meters (111.111 km) in the y direction is 1 degree (of latitude)
// and 111,111 * cos(latitude) meters in the x direction is 1 degree (of longitude).
private static double LatitudeDiffToMeters(double latitudeDiff)
{
return 111111.0 * latitudeDiff;
}
private static double LongitudeDiffToMeters(double longitudeDiff, double latitude)
{
return 111111.0*Math.Cos(latitude)*longitudeDiff;
}
private static double CalculateLatitude(double latitude, double offset)
{
return latitude + offset/111111.0;
}
private static double CalculateLongitude(double longitude, double latitude, double offset)
{
return longitude + offset/(111111.0*Math.Cos(latitude));
}
}

Answer 1

Not sure why the question was voted down!
Anyway,there was an error in my code, i was using degrees instead of radians in the math functions. I also updated the calculations to assume a spherical earth (to work better closer to the poles)
private static double LatitudeDiffToMeters(double latitudeDiff)
{
return (R*latitudeDiff*Math.PI)/180;
}
private static double LongitudeDiffToMeters(double longitudeDiff, double latitude)
{
return (longitudeDiff*Math.PI* R * Math.Cos (Math.PI * latitude / 180))/180;
}
private static double CalculateLatitude(double latitude, double offset)
{
return latitude + ((offset/R) * (180/Math.PI));
}
private static double CalculateLongitude(double longitude, double latitude, double offset)
{
return longitude + offset / (R * Math.Cos (Math.PI * latitude / 180)) * (180 / Math.PI);
}