# 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"#