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
