Question

A triangle has corners at `(8, 5 )`, ( 2, -7)`, and`( 1, -2 )#. If the triangle is reflected across the x-axis, what will its new centroid be?

Answer 1

`(11/3,4/3)`

Explanation:

`"begin by calculating the coordinates of the centroid"`

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

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

`"then the centroid is the average of the x and y"`
`"coordinates of the vertices"`

`"centroid "=[1/3(x_1+x_2+x_3),1/3(y_1+y_2+y_3)]`

`rArr[1/3(8+2+1),1/3(5-7-2)]=(11/3,-4/3)`

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

`• " a point "(x,y)to(x,-y)`

`rArr(11/3,-4/3)to(11/3,4/3)larrcolor(red)"new centroid"`