Question 256338
Triangle DEG has the coordinates D(-1,1), E(5,-1) and G(4,5) Triangle DEG is rotated 90 degrees about the origin to form (triangle)D'E'G'.  State the coordinates of the vertices D', E', and G'.
<pre><font size = 4 color = "indigo"><b>
You didn't state whether the rotation is clockwise or counter-clockwise,
so I'll do it both ways:

Here are the rules:

1. To rotate a point 90° CLOCKWISE about the origin,
Change the sign of the FIRST coordinate, then swap them.

2. To rotate a point 90° COUNTER-CLOCKWISE about the origin,
Change the sign of the SECOND coordinate, then swap them.

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If you want to rotate the triangle 90° CLOCKWISE, follow
rule 1:

D(-1,1) --> D'(1,1) 
E(5,-1) --> E'(-1,-5)
G(4,5)  --> F'(5,-4)

{{{drawing(400,400,-6,6,-6,6, graph(400,400,-6,6,-6,6),

triangle(-1,1,5,-1,4,5), green(triangle(1,1,-1,-5,5,-4))  )}}}

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If you want to rotate the triangle 90° COUNTER-CLOCKWISE, follow
rule 2:

D(-1,1) --> D'(-1,-1) 
E(5,-1) --> E'(1,5)
G(4,5)  --> F'(-5,4)


{{{drawing(400,400,-6,6,-6,6, graph(400,400,-6,6,-6,6),

triangle(-1,1,5,-1,4,5), green(triangle(-1,-1,1,5,-5,4))  )}}}

Edwin</pre>