A triangle has corners at #(3, 4 )#, ( 4, -2)#, and #( 7, -1)#. If the triangle is reflected across the x-axis, what will its new centroid be?
2 Answers
Apr 21, 2018
Explanation:
The centroid is the center of mass, given by the average of the coordinates:
Reflecting through the x axis keeps the x coordinate the same and negates the y coordinate, so we get
Apr 21, 2018
Explanation:
#"given the vertices of a triangle, say"#
#(x_1,y_1),(x_2,y_2),(x_3,y_3)" then"#
#"coordinates of centroid "=[1/3(x_1+x_2+x_3),1/3(y_1+y_2+y_3)]#
#rArr"coordinates "=[1/3(3+4+7),1/3(4-2-1)]#
#color(white)(rArr"coordinates ")=(14/3,1/3)larrcolor(blue)"centroid"#
#"under a reflection in the x-axis"#
#• " a point "(x,y)to(x,-y)#
#rArr(14/3,1/3)to(14/3,-1/3)larrcolor(red)"new centroid"#