Getting position of coordinates and checking if they match
I find the original code overly complicated.  

Here is a revised version of the original test code.  

class Test {

    private $item = [ [ false, true ], [ true, true ] ];

    const VERTICAL_MIDDLE = 421;
    const HORIZONTAL_MIDDLE = 297;

    public function is_quadrant_valid($variable) {
        $down = $variable['y'] &gt; self::VERTICAL_MIDDLE;
        $right = $variable['x'] &gt; self::HORIZONTAL_MIDDLE;

        return $this-&gt;item[$down][$right];
    }

}

$t = new Test();
echo $t-&gt;is_quadrant_valid([ 'y' =&gt; 90, 'x' =&gt; 20 ]) ? 'Valid' : 'Invalid';


This includes a class, which seems to be consistent with the original code.  

This version defines $item as a private property of the class.  Rather than making keys by concatenating strings, I use a two dimensional array system.  This also allows us to arrange $item such that the quadrant organization matches.  

Rather than storing 0s and 1s that we have to convert into false and true values, this just stores true and false directly.  

Instead of using regular variables to store the coordinates of the middle, this uses constants.  

I changed the name of the function to be shorter, but I don't think that it is any less clear.  

Since the original takes a function parameter, it seems that the test version should as well.  This way we could run multiple tests just calling with different values.  

Since we index the arrays with 0 for false and 1 for true, we can simplify the variables.  I renamed them to better match what they hold.  

I find this simpler and easier to read.  You should be able to easily transfer this back to your original code if desired.  

As a general rule, if (is_true()) return true; else return false; can be replaced by return is_true(); which is much shorter.