Question

A triangle has corners at `(6, 5 )`, ( 3, -6)`, and`(8, -1 )#. If the triangle is reflected across the x-axis, what will its new centroid be?

Answer 1

The new centroid is at `(17/3, 2/3)`

Explanation:

The old centroid is at
`x_c=(x_1+x_2+x_3)/3=(6+3+8)/3=17/3`

`y_c=(y_1+y_2+y_3)/3=(5-6-1)/3=-2/3`

The old centroid is at `(17/3, -2/3)`

Since, we are reflecting the triangle across the x-axis, the abscissa of the centroid will not change. Only the ordinate will change. So the new centroid will be at `(17/3, 2/3)`

God bless...I hope the explanation is useful.