A triangle has corners at #(1, 3 )#, ( 8, -4)#, and #(1, -5 )#. If the triangle is reflected across the x-axis, what will its new centroid be?

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Answer 1 · 2016-03-20T06:44:38

New centroid will be #(10/3,2)#.

When a point #(x,y)# is reflected across #x#-axis, new point becomes #(x,-y)#.

Hence corners of new triangle will be #(1,-3)#, #(8,4)# and #(1,5)#.

As centroid of a triangle with sides #(x_1,y_1)#, #(x_2,y_2)# and #(x_3,y_3)# is given by #((x_1+x_2+x_3)/3,(y_1+y_2+y_3)/3)#

New centroid will be #((1+8+1)/3,(-3+4+5)/3)# or #(10/3,2)#.