A triangle has corners at #(3, 9 )#, ( 7, -2)#, and #( 5, -9 )#. If the triangle is reflected across the x-axis, what will its new centroid be?

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Answer 1 · 2017-07-28T07:53:44

The new coordinates of the centroid is #=(5,2/3)#

Let the corners of the triangle be #(x_1,y_1)#, #(x_2,y_2)# and #(x_3,y_3)#

The coordinates of the centroid are

#C=((x_1+x_2+x_3)/2,(y_1+y_2+y_3)/3)#

Here, we have #(3,9)#, #(7,-2)#, and #(5,-9)#

So,

The coordinates of the centroid are #C=((3+7+5)/3,(9-2-9)/3)=(15/3,-2/3)=(5,-2/3)#

The matrix of the reflection acrossthe x-axis is

#M=((1,0),(0,-1))#

Therefore,

The new coordinates of the centroid is

#((x),(y))=((1,0),(0,-1))((5),(-2/3))=((5),(2/3))#