A triangle has corners at #(3, 8 )#, ( 5, -2)#, and #( 1, -1)#. If the triangle is reflected across the x-axis, what will its new centroid be?

1 Answer
Shwetank Mauria
May 14, 2016

Coordinates of centroid will be #(3,-5/3)#

Explanation:

The centroid of a triangle whose vertices are #(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)#

Hence centrid of given triangle is #((3+5+1)/3,(8+(-2)+(-1))/3)# or #(3,5/3)#.

Now, when a point #(x,y)# is reflected across the #x#-axis, its coordinates become #(x,-y)# and hence

New coordinates are #(3,-8)#, #(5,2)# and #(1,1)# and even
coordinates of centroid will have same rule.

Coordinates of centroid will be #(3,-5/3)#

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