A triangle has corners at #(6, 3 )#, ( 8, -2)#, and #(1, -1 )#. If the triangle is reflected across the x-axis, what will its new centroid be?
1 Answer
May 5, 2016
(5 ,0)
Explanation:
The first step here is to find the coordinates of the centroid of the triangle.
Given the 3 vertices of a triangle
#(x_1,y_1),(x_2,y_2),(x_3,y_3)# Then the centroid is calculated as follows:
#color(red)(|bar(ul(color(white)(a/a)color(black)(x_c=1/3(x_1+x_2+x_3), y_c=1/3(y_1+y_2+y_3))color(white)(a/a)|)))# let
#(x_1,y_1)=(6,3),(x_2,y_2)=(8,-2),(x_3,y_3)=(1,-1)#
#rArrx_c=1/3(6+8+1)" and " y_c=1/3(3-2-1)# coordinates of centroid = (5 ,0)
Under a reflection in the x-axis
A point (x ,y) → (x ,-y)
Since the point (5 ,0) is on the x-axis, it's position will remain the same under a reflection in the x-axis.
hence (5 ,0) → (5 ,0)