Question 1191633
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The center of rotation is (-1,4)
We need to translate this center of rotation to the origin (0,0)


Apply the translation rule *[tex \large (x,y) \to (x+1,y-4)] so that (-1,4) moves to (0,0)
This will move (5,3) to (6,-1)


Another way to look at it: imagine that the xy axis is allowed to move but the points (5,3) and (-1,4) stay fixed.
If you moved the xy axis to have (-1,4) placed at the intersection of the axes, then it will give the illuison of movement described earlier.


Now that we have the center of rotation be the origin, we apply this 90 degree counter-clockwise rule:
*[tex \large (x,y) \to (-y,x)]
This means (6,-1) becomes (1,6) after the counter-clockwise quarter turn.


After the rotation is done, we have to undo the translation we initially did. This will get us back to the correct frame of reference so to speak.


The translation we did was
*[tex \large (x,y) \to (x+1,y-4)]
the inverse or opposite translation would be
*[tex \large (x,y) \to (x-1,y+4)]
That moves the point (1,6) to (0,10) which is the final answer.


Visual Confirmation (I used GeoGebra to make the graph):
<img src = "https://i.imgur.com/4XTJS9C.png">


Answer: (0,10)
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