A triangle has corners at #(6, 4 )#, ( 1, -2)#, and #( 4, -1)#. If the triangle is reflected across the x-axis, what will its new centroid be?
1 Answer
Jul 5, 2016
Explanation:
The first step is to find the centroid of the given triangle.
If
#(x_1,y_1),(x_2,y_2)" and " (x_3,y_3)# are the vertices of a triangle,
Then
#color(red)"-----------------------------------------------------"#
x-coordinate of centroid#=1/3(x_1+x_2+x_3)#
and y-coordinate of centroid#=1/3(y_1+y_2+y_3)#
#color(red)"------------------------------------------------------"# here the coordinates of the vertices are (6 ,4), (1 ,-2) and (4 ,-1)
x-coordinate
#=1/3(6+1+4)=11/3# and y-coordinate
#=1/3(4-2-1)=1/3# hence coordinates of centroid
#=(11/3,1/3)# • Under a reflection in the x-axis
a point (x ,y) → (x ,-y)
hence 'new' centroid
#=(11/3,-1/3)#
