Question

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?

Answer 1

`(14/3, -1/3)`

Explanation:

The centroid is the center of mass, given by the average of the coordinates:

`C = \frac 1 3 ((3,4)+(4,-2)+(7,-1)) = ( 14/3, 1/3 )`

Reflecting through the x axis keeps the x coordinate the same and negates the y coordinate, so we get

`C' = (14/3, -1/3)`

Answer 2

`(14/3,-1/3)`

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"`