Find all k points which are closest to origin
This task sounds as if it came directly from an advertisement for the Java 8 streams API:


Sort the points by their distance
Take the minimum k points


This boils down to the following code:

static int[][] kClosest(int[][] points, int k) {
    return Arrays.stream(points)
        .sorted(Comparator.comparing((int[] point) -&gt; point[0] * point[0] + point[1] * point[1]))
        .limit(k)
        .toArray(int[][]::new);
}


That code is written from the top of my head. Since the Java streams API is general-purpose and intended to be highly optimized, it should notice that it only ever needs to remember the \$k\$ smallest elements. You should check this by counting how often the distance function is called. To do that you should extract it to a local method, which is something that your IDE can do for you.

Compared to your code:


I left out the Math.sqrt since the point coordinates are restricted to 10000, which means that the square of the distance can become at most 2e8, which luckily is a bit smaller than Integer.MAX_VALUE.
Calling Math.abs is unnecessary as well.
Making a map of lists may help in pathological cases when the given points all have the same distance. In other cases it can be left out.