# A triangle has corners at #(4, 6 )#, ( 1 , 7)#, and #( 3, -4)#. If the triangle is reflected across the x-axis, what will its new centroid be?

##### 2 Answers

#### Explanation:

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

Given the 3 vertices

#(x_1,y_1),(x_2,y_2)" and " (x_3,y_3)# Then the coords of the centroid are found as follows.

#color(red)(|bar(ul(color(white)(a/a)color(black)(1/3(x_1+x_2+x_3),1/3(y_1+y_2+y_3))color(white)(a/a)|)))# here let

#(x_1,y_1)=(4,6),(x_2,y_2)=(1,7),(x_3,y_3)=(3,-4)# x-coord

#=1/3(4+1+3)=8/3" # and y-coord

#=1/3(6+7-4)=3# coords of centroid

#=(8/3,3)# now, under a reflection in the x-axis

a point (x ,y) → (x ,-y)

hence coords of centroid

#(8/3,3)rArr(8/3,-3)#

New centroid is

#### Explanation:

The centroid of the triangle with corners at

When triangle is reflected across the x-axis, its centroid too is reflected across the x-axis

and as reflection of a point

New centroid is