Question

A triangle has corners at `(0, 5 )`, ( 1, -6)`, and`(8, -4 )#. If the triangle is reflected across the x-axis, what will its new centroid be?

Answer 1

`(3,5/3)`

Explanation:

The centroid `C` also known as barycenter, of a triangle with vertex given as `{a,b,c}` is calculated as:
`C = (a+b+c)/3`. Our triangle has `a = (0,5), b= (1,-6), c = (8,-4)` so
we have `C = (3,-5/3)`. Reflecting the triangle across the `x` axis
implies in reflecting also the barycenter. Choosing the `x` axis facilitate calculations because the `C` point perpendicular projection over the `x` axis is exactly its `x` component with `y = 0`. Call this projected point `C_x = (3,0)`. The reflected point is calculated as `C_r =C + 2 (C_x-C) = (3,5/3)`