# A triangle has corners at #(3, 9 )#, ( 6, -5)#, and #( 4, -1)#. If the triangle is reflected across the x-axis, what will its new centroid be?

##### 1 Answer

Apr 10, 2016

#### Explanation:

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

Given the 3 vertices of a triangle

#(x_1,y_1) , (x_2,y_2) , (x_3,y_3)# the x-coord of centroid

#x_c = color(red)(|bar(ul(color(white)(a/a)color(black)(1/3(x_1+x_2+x_3))color(white)(a/a )|)))# and y-coord of centroid

#y_c=color(red)(|bar(ul(color(white)(a/a)color(black)(1/3(y_1+y_2+y_3))color(white)(a/a)|)))# Here let

#(x_1,y_1)=(3,9),(x_2,y_2)=(6,-5),(x_3,y_3)=(4,-1)# Hence coords of centroid

# = [1/3(3+6+4) , 1/3(9-5-1) ] = (13/3 , 1) # Now under reflection in the x-axis a point (x,y) → (x , -y)

new centroid

#(13/3 , 1) → (13/3 , -1)#