# A triangle has corners at #(3, 8 )#, ( 2, -2)#, and #( 2, -1)#. If the triangle is reflected across the x-axis, what will its new centroid be?

##### 1 Answer

Mar 13, 2016

#### Explanation:

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)# x-coord of centroid

# = 1/3(x_1+x_2+x_3)# and y-coord of centroid

# = 1/3(y_1+y_2+y_3)# here let

#(x_1,y_1)=(3,8) , (x_2,y_2)=(2,-2). (x_3,y_3)=(2,-1)# hence coords of centroid

# = [1/3(3+2+2),1/3(8-2-1)] = (7/3,5/3)# Now under reflection in the x-axis a point (x,y) → (x,-y)

new centroid :

#(7/3,5/3) → (7/3,-5/3) #