A triangle has corners at #(7, 2 )#, ( 9, -7)#, and #(1, 4 )#. If the triangle is reflected across the x-axis, what will its new centroid be?

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Answer 1 · 2016-04-19T09:30:00

Coordinates of new centroid are #(17/3,1/3)#

Reflection of a point #(x,y)# in #x#-axis is #(x,-y)#.

Hence reflection of a triangle having corners at #(7,2)#, #(9,-7)# and #(1,4)# will be a triangle with corners at #(7,-2)#, #(9,7)# and #(1,-4)#.

As coordinates of centroid of a triangle with points at #(x_1,y_1)#, #(x_2,y_2)# and #(x_3,y_3)# is #((x_1+x_2+x_3)/3,(y_1+y_2+y_3)/3)# and hence

coordinates of new centroid are #((7+9+1)/3,(-2+7-4)/3)# or #(17/3,1/3)#