Question

A triangle has corners at `(3, 5 )`, ( 6, 2)`, and`( 4, 3)#. If the triangle is reflected across the x-axis, what will its new centroid be?

Answer 1

`(13/3,-10/3)`

Explanation:

`"given the coordinates of the vertices of a triangle"`

`(x_1,y_1),(x_2,y_2),(x_3,y_3)`

`"then the coordinates of the centroid are"`

`•color(white)(x)[1/3(x_1+x_2+x_3),1/3(y_1+y_2+y_3)]`

`"here "(x_1,y_1)=(3,5),(x_2,y_2)=(6,2),(x_3,y_3)=(4,3)`

`"hence coordinates of centroid are"`

`[1/3(3+6+4),1/3(5+2+3)]=(13/3,10/3)`

`"under a reflection in the x-axis"`

`• " a point "(x,y)to(x,-y)`

`rArr(13/3,10/3)to(13/3,-10/3)larrcolor(red)"new centroid"`