Question 1191633
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Here is a far less formal method for answering the question.<br>
The displacement (I will avoid the use of the formal word "vector") from the center of the rotation (-1,4) to the given point (5,3) is "6 right, down 1".<br>
When the point is rotated 1/4 turn counterclockwise about (-1,4), the "6 right" becomes "up 6" and the "down 1" becomes "right 1".<br>
So the image of the point (5,3) under the given rotation is (-1+1,4+6) = (0,10).<br>
ANSWER: (0,10)<br>