Edit in JSFiddle

// create a map
var map = $("#map").geomap({
    center: [-71.0595678, 42.3604823],
    zoom: 8
});

// append a red Point
var pt = {
    type: "Point",
    coordinates: [-71, 42]
};
map.geomap("append", pt);

// append a red LineString
var line = {
    type: "LineString",
    coordinates: [
        [-71.5, 42],
        [-72, 41.5]
        ]
};
map.geomap("append", line);

// append a red Polygon
var poly = {
    type: "Polygon",
    coordinates: [[
        [-72.5, 41.7],
        [-72.3, 41.3],
        [-72.7, 41.3],
        [-72.5, 41.7]
        ]]
};
map.geomap("append", poly);

// distance calculations between all red shapes
$(".rpt-2-rpt-distance").text($.geo.distance(pt, pt));
$(".rpt-2-line-distance").text($.geo.distance(pt, line));
$(".rpt-2-poly-distance").text($.geo.distance(pt, poly));

$(".line-2-rpt-distance").text($.geo.distance(line, pt));
$(".line-2-line-distance").text($.geo.distance(line, line));
$(".line-2-poly-distance").text($.geo.distance(line, poly));

$(".poly-2-rpt-distance").text($.geo.distance(poly, pt));
$(".poly-2-line-distance").text($.geo.distance(poly, line));
$(".poly-2-poly-distance").text($.geo.distance(poly, poly));

// contains relationships between all red shapes
$(".rpt-2-rpt-contains").text($.geo.contains(pt, pt));
$(".rpt-2-line-contains").text($.geo.contains(pt, line));
$(".rpt-2-poly-contains").text($.geo.contains(pt, poly));

$(".line-2-rpt-contains").text($.geo.contains(line, pt));
$(".line-2-line-contains").text($.geo.contains(line, line));
$(".line-2-poly-contains").text($.geo.contains(line, poly));

$(".poly-2-rpt-contains").text($.geo.contains(poly, pt));
$(".poly-2-line-contains").text($.geo.contains(poly, line));
$(".poly-2-poly-contains").text($.geo.contains(poly, poly));

// append a green Point inside the red Polygon
var gpt = {
    type: "Point",
    coordinates: [-72.5, 41.6]
};
map.geomap("append", gpt, {
    color: "green"
});

// append a green LineString inside the red Polygon
var gline = {
    type: "LineString",
    coordinates: [
        [-72.55, 41.5],
        [-72.45, 41.5]
        ]
};
map.geomap("append", gline, {
    color: "green",
    strokeWidth: "3px"
});

// append a green Polygon completely inside the red Polygon
var gpoly = {
    type: "Polygon",
    coordinates: [[
        [-72.55, 41.45],
        [-72.5, 41.35],
        [-72.65, 41.35],
        [-72.55, 41.45]
        ]]
};
map.geomap("append", gpoly, {
    color: "green",
    strokeWidth: "3px"
});

// contains relationships between the red polygon & some green shapes
// these all return true because the red polygon completely contains all of them
$(".poly-2-gpt-contains").text($.geo.contains(poly, gpt));
$(".poly-2-gline-contains").text($.geo.contains(poly, gline));
$(".poly-2-gpoly-contains").text($.geo.contains(poly, gpoly));

// append a blue Polygon partially inside the red Polygon
var bpoly = {
    type: "Polygon",
    coordinates: [[
        [-72.35, 41.45],
        [-72.25, 41.35],
        [-72.45, 41.35],
        [-72.35, 41.45]
        ]]
};
map.geomap("append", bpoly, {
    color: "blue",
    strokeWidth: "3px"
});

// contains relationships between the red polygon the blue polygon
// this returns false because the red polygon does not completely contain the blue one
$(".poly-2-bpoly-contains").text($.geo.contains(poly, bpoly));

// centroid calculations for all red shapes and the green and blue polygons
// the centroid function returns a full GeoJSON Point object
// but we will only show the coordinates array on the page
$(".rpt-centroid").text($.geo.centroid(pt).coordinates.join(", "));
$(".rline-centroid").text($.geo.centroid(line).coordinates.join(", "));
$(".rpoly-centroid").text($.geo.centroid(poly).coordinates.join(", "));
$(".gpoly-centroid").text($.geo.centroid(gpoly).coordinates.join(", "));
$(".bpoly-centroid").text($.geo.centroid(bpoly).coordinates.join(", "));
<div>
    <div id="map">
    </div>
    <div class="info">
        <h1>
            geometry functions</h1>
        <p>This example appends a few Points, LineStrings, and Polygons. It then calculates some relationships and info about the shapes using the geometry functions in the $.geo namespace.</p>
        <div class="calc">
            <table>
                <tr>
                    <td></td>
                    <th>distance</th>
                </tr>
                <tr>
                    <th><span class="red">pt</span>, <span class="red">pt</span></th>
                    <td class="rpt-2-rpt-distance"></td>
                </tr>
                <tr>
                    <th><span class="red">pt</span>, <span class="red">line</span></th>
                    <td class="rpt-2-line-distance"></td>
                </tr>
                <tr>
                    <th><span class="red">pt</span>, <span class="red">poly</span></th>
                    <td class="rpt-2-poly-distance"></td>
                </tr>
                <tr>
                    <th><span class="red">line</span>, <span class="red">pt</span></th>
                    <td class="line-2-rpt-distance"></td>
                </tr>
                <tr>
                    <th><span class="red">line</span>, <span class="red">line</span></th>
                    <td class="line-2-line-distance"></td>
                </tr>
                <tr>
                    <th><span class="red">line</span>, <span class="red">poly</span></th>
                    <td class="line-2-poly-distance"></td>
                </tr>
                <tr>
                    <th><span class="red">poly</span>, <span class="red">pt</span></th>
                    <td class="poly-2-rpt-distance"></td>
                </tr>
                <tr>
                    <th><span class="red">poly</span>, <span class="red">line</span></th>
                    <td class="poly-2-line-distance"></td>
                </tr>
                <tr>
                    <th><span class="red">poly</span>, <span class="red">poly</span></th>
                    <td class="poly-2-poly-distance"></td>
                </tr>
            </table>
        </div>
        <div class="calc">
            <table>
                <tr>
                    <td></td>
                    <th>contains</th>
                </tr>
                <tr>
                    <th><span class="red">pt</span>, <span class="red">pt</span></th>
                    <td class="rpt-2-rpt-contains"></td>
                </tr>
                <tr>
                    <th><span class="red">pt</span>, <span class="red">line</span></th>
                    <td class="rpt-2-line-contains"></td>
                </tr>
                <tr>
                    <th><span class="red">pt</span>, <span class="red">poly</span></th>
                    <td class="rpt-2-poly-contains"></td>
                </tr>
                <tr>
                    <th><span class="red">line</span>, <span class="red">pt</span></th>
                    <td class="line-2-rpt-contains"></td>
                </tr>
                <tr>
                    <th><span class="red">line</span>, <span class="red">line</span></th>
                    <td class="line-2-line-contains"></td>
                </tr>
                <tr>
                    <th><span class="red">line</span>, <span class="red">poly</span></th>
                    <td class="line-2-poly-contains"></td>
                </tr>
                <tr>
                    <th><span class="red">poly</span>, <span class="red">pt</span></th>
                    <td class="poly-2-rpt-contains"></td>
                </tr>
                <tr>
                    <th><span class="red">poly</span>, <span class="red">line</span></th>
                    <td class="poly-2-line-contains"></td>
                </tr>
                <tr>
                    <th><span class="red">poly</span>, <span class="red">poly</span></th>
                    <td class="poly-2-poly-contains"></td>
                </tr>
            </table>
        </div>
        <div class="calc">
            <table>
                <tr>
                    <td></td>
                    <th>contains</th>
                </tr>
                <tr>
                    <th><span class="red">poly</span>, <span class="green">pt</span></th>
                    <td class="poly-2-gpt-contains"></td>
                </tr>
                <tr>
                    <th><span class="red">poly</span>, <span class="green">line</span></th>
                    <td class="poly-2-gline-contains"></td>
                </tr>
                <tr>
                    <th><span class="red">poly</span>, <span class="green">poly</span></th>
                    <td class="poly-2-gpoly-contains"></td>
                </tr>
                <tr>
                    <th><span class="red">poly</span>, <span class="blue">poly</span></th>
                    <td class="poly-2-bpoly-contains"></td>
                </tr>
            </table>
        </div>
        <div class="calc">
            <table>
                <tr>
                    <td></td>
                    <th>centroid</th>
                </tr>
                <tr>
                    <th><span class="red">pt</span></th>
                    <td class="rpt-centroid"></td>
                </tr>
                <tr>
                    <th><span class="red">line</span></th>
                    <td class="rline-centroid"></td>
                </tr>
                <tr>
                    <th><span class="red">poly</span></th>
                    <td class="rpoly-centroid"></td>
                </tr>
                <tr>
                    <th><span class="green">poly</span></th>
                    <td class="gpoly-centroid"></td>
                </tr>
                <tr>
                    <th><span class="blue">poly</span></th>
                    <td class="bpoly-centroid"></td>
                </tr>
            </table>
        </div>
    </div>
</div>
html
{
    font:13px/1.231 Calibri,Arial,sans-serif; *font-size:small;
}

.info 
{
    background: #fff;
    border-radius: 8px;
    box-shadow: -4px 4px #444;
    opacity: .8;
    padding: 8px;
    width: 95%;
}
#map
{
    position: fixed;
    left: 0;
    top: 0;
    right: 0;
    bottom: 0;
}
.calc
{
    display: inline-block;
    vertical-align: top;
}
td
{
    max-width: 96px;
    overflow: hidden;
    text-overflow: ellipsis;
}
.red { color: #c00; }
.green { color: #0c0; }
.blue { color: #00c; }

External resources loaded into this fiddle: