A triangle has corners at #(1, 2 )#, ( 5, -9)#, and #( 2, -1)#. If the triangle is reflected across the x-axis, what will its new centroid be?

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Answer 1 · 2016-03-11T09:55:31

New centroid is #(8/3,8/3)#

The centroid of the triangle with corners at #(1,2)#, #(5,-9)# and #(2, -1 )# is

#((1+5+2)/3,(2+(-9)+(-1))/3)# or #(8/3,-8/3)#

When triangle is reflected across the x-axis, its centroid too is reflected across the x-axis

and as reflection of a point #(x_1,y_1)# in x-axis is #(x_1,-y_1)#,

new centroid is #(8/3,8/3)#