A triangle has corners at #(9, 4 )#, ( 5, -9)#, and #( 2, -3)#. If the triangle is reflected across the x-axis, what will its new centroid be?
1 Answer
Jul 10, 2016
Explanation:
The first step is to calculate the coordinates of the existing centroid.
Given the 3 vertices of a triangle
#(x_1,y_1),(x_2,y_2)" and " (x_3,y_3)# x-coordinate of centroid =
#color(red)(|bar(ul(color(white)(a/a)color(black)(1/3(x_1+x_2+x_3))color(white)(a/a)|)))# y-coordinate of centroid =
#color(red)(|bar(ul(color(white)(a/a)color(black)(1/3(y_1+y_2+y_3))color(white)(a/a)|)))# Basically, this is the average of the x and y-coordinates of the vertices.
Thus x-coordinate =
#1/3(9+5+2)=16/3# and y-coordinate =
#1/3(4-9-3)=-8/3# coordinates of centroid
#=(16/3,-8/3)# Under a reflection in the x-axis
a point (x ,y) → (x ,-y)
hence
#(16/3,-8/3)to(16/3,8/3)" new centroid"#
