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A triangle with vertices A(-2,_1), B(-1, 4), and C(5, 0) is rotated 90 degrees counter-clockwise about vertex B. Find the co-cordinates of the image of vertex A.

neurolover25  Feb 24, 2018
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There may be other ways to do this, but....one way is to position B at the origin  and position the other points accordingly

 

So A  becomes  ( -2 + 1, 1 - 4)  =  ( - 1, - 3)

And C becomes ( 5 + 1, 0  - 4)  =  (6, - 4)

 

The slope of A  from the origin is  ( -3/ -1)  =  (3/1)

Rotated 90° counter-clockwise  produces     (-1/3)  = (-3, 1)

 

The slope of C from the origin produces ( -4/6)

Rotated 90° counter=clockwise prouduces ( 6/4)  =  (6, 4)

 

So......re-positioning the points, we have

 

B = ( -1 , 4)

A =  ( -3- 1, 1 + 4)  =  ( -4, 5)

C = (6 - 1, 4 + 4)  =  ( 5, 8)

 

cool cool cool

CPhill  Feb 24, 2018

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