# A triangle has corners at #(8, 3 )#, ( 5, -8)#, and #(7, -4 )#. If the triangle is reflected across the x-axis, what will its new centroid be?

##### 1 Answer

Oct 23, 2016

#### Explanation:

The first step is to find the coordinates of the centroid,

#(x_c,y_c)# Given that the vertices of a triangle are

#(x_1,y_1),(x_2,y_2),(x_3,y_3)# Then.

#x_c=1/3(x_1+x_2+x_3)" the average of the x-coordinates"# and

#y_c=1/3(y_1+y_2+y_3)" the average of the y-coordinates"# Here.

#(x_1,y_1)=(8,3),(x_2,y_2)=(5,-8), (x_3,y_3)=(7,-4)#

#rArrx_c=1/3(8+5+7)=20/3# and

#y_c=1/3(3-8-4)=-3# coordinates of centroid

#=(20/3,-3)# Under reflection in the x-axis, a point (x ,y) → (x ,-y)

#rArr(20/3,-3)to(20/3,3)#