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

1 Answer
Shwetank Mauria
Apr 20, 2016

Coordinates of new centroid are #(7/3,0)#

Explanation:

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

Hence reflection of a triangle having corners at #(2,7)#, #(5,-2)# and #(1,-5)# will be a triangle with corners at #(2,-7)#, #(5,2)# and #(1,5)#.

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 #((2+5+1)/3,(-7+2+5)/3)# or #(7/3,0)#

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