identify zip codes that fall within latitude and l

I have several data frames in R. The first data frame contains the computed convex hull of a set of lat and long coordinates by market (courtesy of chull in R). It looks like this:

MyGeo<- "Part of Chicago & Wisconsin"
Longitude <- c(-90.31914,  -90.61911,  -89.37842,  -88.0988,  -87.44875)
Latitude <- c(38.45781, 38.80097, 43.07961, 43.0624,41.49182)

dat <- data.frame(Longitude, Latitude, MyGeo)

The second has zip codes by their latitude and longitudinal coordinates (courtesy of the US census website). It looks like this:

CensuseZip <- c("SomeZipCode1","SomeZipCode2","SomeZipCode3","SomeZipCode4","SomeZipCode5","SomeZipCode6","SomeZipCode7") 
Longitude2 <- c(-131.470425,-133.457924,-131.693453,-87.64957,-87.99734,-87.895,-88.0228)
Latitude2 <- c(55.138352,56.239062,56.370538,41.87485,42.0086,42.04957,41.81055)

cen <- data.frame(Longitude2, Latitude2,   CensuseZip)

Now I believe the first data table provides me with a polygon, or a border, that I should be able to use to identify zip codes that fall within that border. Ideally, I would want to create a third data table that looks something like this:

 Longitude2 Latitude2    CensusZip                        MyGeo
-131.470425 55.138352 SomeZipCode1  
-133.457924 56.239062 SomeZipCode2  
-131.693453 56.370538 SomeZipCode3
-87.64957    41.87485 SomeZipCode4  Part of Chicago & Wisconsin 
-87.99734     42.0086 SomeZipCode5  Part of Chicago & Wisconsin 
-87.895      42.04957 SomeZipCode6  Part of Chicago & Wisconsin 
-88.0228     41.81055 SomeZipCode7  Part of Chicago & Wisconsin

In essence, I am looking to identify all the zip codes that fall between the blue (see clickable image below) long and lat points. While it is visualized below, I am actually looking for the table described above.

However... I am having trouble doing this... I have tried using the below packages and script:

library(rgeos)
library(sp)
library(rgdal)

coordinates(dat) <- ~ Longitude + Latitude
coordinates(cen) <- ~ Longitude2 + Latitude2

over(cen, dat)

but I receive all NAs.

I use library(sf) to solve this type of point-in-polygon problem (sf is the successor to sp).

The function sf::st_intersection() gives you the intersection of two sf objects. In your case you can construct separate POLYGON and POINT sf objects.

library(sf)

Longitude <- c(-90.31914,  -90.61911,  -89.37842,  -88.0988,  -87.44875)
Latitude <- c(38.45781, 38.80097, 43.07961, 43.0624,41.49182)

## closing the polygon
Longitude[length(Longitude) + 1] <- Longitude[1]
Latitude[length(Latitude) + 1] <- Latitude[1]

## construct sf POLYGON
sf_poly <- sf::st_sf( geometry = sf::st_sfc( sf::st_polygon( x = list(matrix(c(Longitude, Latitude), ncol = 2)))) )

## construct sf POINT
sf_points <- sf::st_as_sf( cen, coords = c("Longitude2", "Latitude2"))

sf::st_intersection(sf_points, sf_poly)

# Simple feature collection with 4 features and 1 field
# geometry type:  POINT
# dimension:      XY
# bbox:           xmin: -88.0228 ymin: 41.81055 xmax: -87.64957 ymax: 42.04957
# epsg (SRID):    NA
# proj4string:    NA
# CensuseZip                   geometry
# 4 SomeZipCode4 POINT (-87.64957 41.87485)
# 5 SomeZipCode5  POINT (-87.99734 42.0086)
# 6 SomeZipCode6   POINT (-87.895 42.04957)
# 7 SomeZipCode7  POINT (-88.0228 41.81055)
# Warning message:
#   attribute variables are assumed to be spatially constant throughout all geometries

The result is all the points which are inside the polygon

You can also use sf::st_join(sf_poly, sf_points) to give the same result

And, the function sf::st_intersects(sf_points, sf_poly) will return a list saying whether the given POINT is inside the polygon

sf::st_intersects(sf_points, sf_poly)

# Sparse geometry binary predicate list of length 7, where the predicate was `intersects'
#  1: (empty)
# 2: (empty)
# 3: (empty)
# 4: 1
# 5: 1
# 6: 1
# 7: 1

Which you can use as an index / identifier of the original sf_points object to add a new column on

is_in <- sf::st_intersects(sf_points, sf_poly)

sf_points$inside_polygon <- as.logical(is_in)

sf_points
# Simple feature collection with 7 features and 2 fields
# geometry type:  POINT
# dimension:      XY
# bbox:           xmin: -133.4579 ymin: 41.81055 xmax: -87.64957 ymax: 56.37054
# epsg (SRID):    NA
# proj4string:    NA
# CensuseZip                   geometry inside_polygon
# 1 SomeZipCode1 POINT (-131.4704 55.13835)             NA
# 2 SomeZipCode2 POINT (-133.4579 56.23906)             NA
# 3 SomeZipCode3 POINT (-131.6935 56.37054)             NA
# 4 SomeZipCode4 POINT (-87.64957 41.87485)           TRUE
# 5 SomeZipCode5  POINT (-87.99734 42.0086)           TRUE
# 6 SomeZipCode6   POINT (-87.895 42.04957)           TRUE
# 7 SomeZipCode7  POINT (-88.0228 41.81055)           TRUE