A triangle has corners at #(6, 4 )#, ( 2, 5)#, and #( 7, -1)#. If the triangle is reflected across the x-axis, what will its new centroid be?

1 Answer
Shwetank Mauria
Jun 13, 2017

Coordinates of new centroid are #(5,-8/3)#.

Explanation:

The coordinates of the centroid of a triangle, whose corners are #(x_1,y_1)#, #(x_2,y_2)# and #(x_3,y_3)#, are #((x_1+x_2+x_3)/3,(y_1+y_2+y_3)/3)#.

As such coordinates of centroid of the triangle with corners at #(6,4)#, #(2,5)# and #(7,-1)# are #((6+2+7)/3,(4+5-1)/3)# i.e. #(5,8/3)#.

When a point #(x,y)# is reflected across #x#-axis, its coordinates change to #(x,-y)#.

Hence new coordinates of corners of the triangle are #(6,-4)#, #(2,-5)# and #(7,1)# and coordinates of new centroid are #((6+2+7)/3,(-4-5+1)/3)# i.e. #(5,-8/3)#.

Observe that centroid too is reflected across #x#-axis.

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