# A triangle has corners at #(8, 5 )#, ( 2, -7)#, and #( 1, -2 )#. If the triangle is reflected across the x-axis, what will its new centroid be?

##### 1 Answer

May 18, 2018

#### Explanation:

#"begin by calculating the coordinates of the centroid"#

#"given the coordinates of the vertices of a triangle say"#

#(x_1,y_1),(x_2,y_2)" and "(x_3,y_3)#

#"then the centroid is the average of the x and y"#

#"coordinates of the vertices"#

#"centroid "=[1/3(x_1+x_2+x_3),1/3(y_1+y_2+y_3)]#

#rArr[1/3(8+2+1),1/3(5-7-2)]=(11/3,-4/3)#

#"under a reflection in the x-axis"#

#• " a point "(x,y)to(x,-y)#

#rArr(11/3,-4/3)to(11/3,4/3)larrcolor(red)"new centroid"#