There are an infinite number of such points. One of the easiest to write coordinates for is the one that is on the same horizontal line. Its x-value will be 4 less that that of Q.
(-2, -2.5) is one such point
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<em>Additional comment</em>
All of the points that could be solutions are on that portion of a circle with radius 4 and center Q that lies in quadrant III. They make up the red arc in the attachment.