# Coordinate System choice for Nearest Neighbor

Here's an interesting scenario I came upon yesterday and I wanted to throw it out as a question to try help me visualize what is happening.

I have a single point (a person, say) who is looking for the nearest transit station. The person's location is in Lat/Long and the transit station is a dataset in UTM.

To do a nearest neighbor I need to reproject either the person into UTM (to match the transit dataset) or the transit dataset into Lat/Long (to match the person).

If I reproject the person to UTM, the nearest neighbor tells me the nearest transit station is X

If I reproject the transit stations to Lat/Long, the nearest neighbor tells me the nearest transit station is Y

So... does it make sense that the nearest neighbor can be different depending on which coordinate system you are working in? My gut feeling is yes, because Lat/Long is a geographic coordinate system and UTM isn't.

Am I right? I think so but am just having problems visualizing why! In particular, which one of the results is "correct"?

• Hi Mark, would you not get inconsistent results because the GCS is a nonlinear unit type (degrees), opposed to metres? – Corey Pembleton Dec 10 '15 at 15:41
• Lat/Long Distance based on which formula? movable-type.co.uk/scripts/latlong-vincenty.html#direct might be of interest noting the different ellipsoids have different results – Mapperz Dec 10 '15 at 15:55
• @CoreyPembleton - probably, yes. But which one is closer to reality? I can see that the result could be different, I guess I'm most confused about which is the better result. Would it be better to convert both to an equal distance coordinate system? I'm most interested because it's something I hadn't even thought about - until I found an example with that different result. – Mark Ireland Dec 10 '15 at 16:00
• @MarkIreland Yeah I would think that converting both into a projected equidistant coordinate system would be best. Are you using Arc? This tool maybe can be used if you convert points from both into new layers and run it: resources.arcgis.com/EN/HELP/MAIN/10.2/index.html#//… – Corey Pembleton Dec 10 '15 at 16:15
• If you're using ArcGIS, measure the distance in ArcMap (using geodesic distance) with the measure tool as a check. – mkennedy Dec 10 '15 at 17:08