A triangle has corners at #(2, 7 )#, ( 5, -2)#, and #( 1, -1)#. If the triangle is reflected across the x-axis, what will its new centroid be?

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Answer 1 · 2016-03-07T07:58:07

The new centroid #(8/3, -4/3)#

From the old centroid :(8/3, 4/3)

#x=(x_1+x_2+x_3)/3=(1+2+5)/3=8/3#
#y=(y_1+y_2+y_3)/3=(-1+7-2)/3=4/3#

Only the ordinate 4/3 will change to -4/3 located at the 4th quadrant.
So the new centroid is #(8/3, -4/3)#

God bless...I hope the explanation is useful.