A triangle has corners at #(4, 3 )#, ( 7, -4)#, and #(6, -5 )#. If the triangle is reflected across the x-axis, what will its new centroid be?

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Answer 1 · 2016-03-01T10:15:50

Centroid will be at #(17/3,2)#

Centroid of a triangle, whose vertices are #(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)#.

When a point #(x,y)# is reflected in #x# axis, coordinated of reflection point are #(x,-y)#.

Hence coordinates of corners of triangle #(4,3)#, #(7,-4)# and #(6,-5)# on reflection become #(4,-3)#, #(7,4)# and #(6,5)#.

Centroid of reflected triangle will be

#((4+7+6)/3, (-3+4+5)/3)# or #(17/3,2)#