A triangle has corners at #(3, 7 )#, ( 5, 1)#, and #( 6, 3)#. If the triangle is reflected across the x-axis, what will its new centroid be?

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Answer 1 · 2018-06-04T11:30:40

#color(blue)((14/3,-11/3)#

First we need to find the centroid. The centroid can be found by finding the arithmetic mean of the #x# and #y# coordinates:

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

Using given points:

#((3+5+6)/3,(7+1+3)/3)=>(14/3,11/3)#

Let #C=(14/3,11/3)#

A reflection in the line #y=0# ( x axis ) maps:

#(x,y)->(x,-y)#

Therefore:

#C->C'=(14/3,11/3)->(14/3,-11/3)#