A triangle has corners at #(0, 5 )#, ( 1, -6)#, and #(8, -4 )#. If the triangle is reflected across the x-axis, what will its new centroid be?

1 Answer
Cesareo R.
May 18, 2016

#(3,5/3)#

Explanation:

The centroid #C# also known as barycenter, of a triangle with vertex given as #{a,b,c}# is calculated as:
#C = (a+b+c)/3#. Our triangle has #a = (0,5), b= (1,-6), c = (8,-4)# so
we have #C = (3,-5/3)#. Reflecting the triangle across the #x# axis
implies in reflecting also the barycenter. Choosing the #x# axis facilitate calculations because the #C# point perpendicular projection over the #x# axis is exactly its #x# component with #y = 0#. Call this projected point #C_x = (3,0)#. The reflected point is calculated as #C_r =C + 2 (C_x-C) = (3,5/3)#

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