A triangle has corners at #(8, 1 )#, ( 5, -8)#, and #(7, -2 )#. If the triangle is reflected across the x-axis, what will its new centroid be?

1 Answer
Dec 6, 2016

The coordinates of the centroid of the triangle after it has been reflected over the #x# axis are #(20/3,3)#.

Explanation:

The reflection of #(x,y)# over the #x# axis is #(x, -y)#.

If a triangle has vertices of #(8,1), (5,-8), (7,-2)#,

the vertices after reflecting it over the #x# axis are #(8,-1), (5,8), (7,2)#.

To find the coordinates of a centroid of a triangle with vertices at #(x_1, y_1), (x_2,y_2), (x_3,y_3)#, use the formula

#(x,y)_"centroid"= ((x_1+x_2+x_3)/3, (y_1+y_2+y_3)/3)#

#(x,y)_"centroid"=((8+5+7)/3, (-1+8+2)/3)=(20/3,3)#