I do not believe my math is incorrect. This is seems like it could be a projection issue.

I start with the following two coordinates ( lon, lat in degrees )

a: [37.821055535000085, -46.84417083099993] b: [37.89112389400009, -46.64967213299991]

When visualized with geopandas, the lineSegment defined by the points looks like:

path = 'data.geo.json'
data = json.load( open( path, "r" ) )
gdf = geopandas.GeoDataFrame.from_features( data, crs = 4326 )

What is drawn here is correct.

I want to extend this line segment in both directions and draw the perpendicular line segment.

To do this, I am using turf and some math:

  const direction = [b[0] - a[0], b[1] - a[1]]
  const length = Math.sqrt(Math.pow(direction[0], 2) + Math.pow(direction[1], 2))

  direction[0] = direction[0] / length
  direction[1] = direction[1] / length

  const b2 = [a[0] + direction[0] * length, a[1] + direction[1] * length]

  const lineSegment = turf.lineString([a, b2])

  const perpendicularDirection = [-direction[1], direction[0]]
  const boxDiagonalLength = length * 2
  let boxPoint = a

  const iFactor = direction[0] * boxDiagonalLength
  const jFactor = direction[1] * boxDiagonalLength
  const normalLineEndA = [boxPoint[0] + iFactor, boxPoint[1] + jFactor]
  const normalLineEndB = [boxPoint[0] - iFactor, boxPoint[1] - jFactor]
  const normalLine = turf.lineString([normalLineEndA, normalLineEndB])

  const piFactor = perpendicularDirection[0] * boxDiagonalLength
  const pjFactor = perpendicularDirection[1] * boxDiagonalLength
  const pNormalLineEndA = [boxPoint[0] + piFactor, boxPoint[1] + pjFactor]
  const pNormalLineEndB = [boxPoint[0] - piFactor, boxPoint[1] - pjFactor]
  const pNormalLine = turf.lineString([pNormalLineEndA, pNormalLineEndB])

When I visualize the extended line ( normalLine ) and the perpendicular line to the extended line ( pNormalLine ) with geopandas, it produces:

The extended line is shifted to the right. The line that should be perpendicular isn't.

I expected the extended line to overlap the line segment and for the perpendicular line to be perpendicular. Additionally, I would expect the point of intersection to be at a.

I am not sure what is going wrong. I am guessing there is a fundamental concept I am missing.

What am I missing?