Question 872206
<pre>

I'll do it for (2,3).  You do it for (1,3)

What we'll show is that rotation of 90° counterclockwise 
swaps the coordinates and changes the sign of the new 
x-coordinate.

{{{matrix(7,1,
On, graph, paper, plot, the, point, "(2,3)")}}}{{{drawing(160,160,-5,5,-5,5, grid(1),


circle(2,3,0.25),circle(2,3,0.23),circle(2,3,0.21),circle(2,3,0.19),circle(2,3,0.17),circle(2,3,0.15),circle(2,3,0.08),circle(2,3,0.03)

)}}}{{{matrix(10,1,

Draw, a, line, from, the, origin, to, the, point, "(2,3)")}}}{{{drawing(160,160,-5,5,-5,5, grid(1),
green(line(0,0,2,3)),

circle(2,3,0.25),circle(2,3,0.23),circle(2,3,0.21),circle(2,3,0.19),circle(2,3,0.17),circle(2,3,0.15),circle(2,3,0.08),circle(2,3,0.03)

)}}}{{{matrix(14,1,

Put,sharp, point,of,compass,at, origin,and,pencil,on,"(2,3)",swing,counter-clockwise,arc)}}}{{{drawing(160,160,-5,5,-5,5, grid(1),
green(line(0,0,2,3)),

circle(2,3,0.25),circle(2,3,0.23),circle(2,3,0.21),circle(2,3,0.19),circle(2,3,0.17),circle(2,3,0.15),circle(2,3,0.08),circle(2,3,0.03),
red(arc(0,0,2sqrt(13),-2sqrt(13),40,165))

)}}}


{{{matrix(8,1,

Draw, a, line, perpendicular, to, the, other, one)}}}{{{drawing(160,160,-5,5,-5,5, grid(1),
green(line(0,0,2,3),line(-3.6,2.4,0,0)),

circle(2,3,0.25),circle(2,3,0.23),circle(2,3,0.21),circle(2,3,0.19),circle(2,3,0.17),circle(2,3,0.15),circle(2,3,0.08),circle(2,3,0.03),
red(arc(0,0,2sqrt(13),-2sqrt(13),40,165))

)}}}{{{matrix(10,1,

Mark, the, point, where, that, perpendicular, line, intersects, the, arc)}}}{{{drawing(160,160,-5,5,-5,5, grid(1),
green(line(0,0,2,3),line(-3.6,2.4,0,0)),

circle(2,3,0.25),circle(2,3,0.23),circle(2,3,0.21),circle(2,3,0.19),circle(2,3,0.17),circle(2,3,0.15),circle(2,3,0.08),circle(2,3,0.03),
red(arc(0,0,2sqrt(13),-2sqrt(13),40,165)),

circle(-3,2,0.25),circle(-3,2,0.23),circle(-3,2,0.21),circle(-3,2,0.29),circle(-3,2,0.27),circle(-3,2,0.25),circle(-3,2,0.08),circle(-3,2,0.03)

)}}}{{{matrix(9,1,

We,see,that,the,image,is,the,point,"(-3,2)")}}}

As I said above, the thing to observe is that:

1. Rotation of 90° counterclockwise swaps the coordinates
and changes the sign of the new x-coordinate.

(2,3) became (-3,2)

Do the same thing clockwise and you'll find:

2. Rotation of 90° clockwise swaps the coordinates and
changes the sign of the new y-coordinate.

(2,3) will become (3,-2)

Edwin</pre>