Question

A triangle has corners at `(6, 4 )`, ( 2, 5)`, and`( 7, -1)#. If the triangle is reflected across the x-axis, what will its new centroid be?

Answer 1

Coordinates of new centroid are `(5,-8/3)`.

Explanation:

The coordinates of the centroid of a triangle, whose corners are `(x_1,y_1)`, `(x_2,y_2)` and `(x_3,y_3)`, are `((x_1+x_2+x_3)/3,(y_1+y_2+y_3)/3)`.

As such coordinates of centroid of the triangle with corners at `(6,4)`, `(2,5)` and `(7,-1)` are `((6+2+7)/3,(4+5-1)/3)` i.e. `(5,8/3)`.

When a point `(x,y)` is reflected across `x`-axis, its coordinates change to `(x,-y)`.

Hence new coordinates of corners of the triangle are `(6,-4)`, `(2,-5)` and `(7,1)` and coordinates of new centroid are `((6+2+7)/3,(-4-5+1)/3)` i.e. `(5,-8/3)`.

Observe that centroid too is reflected across `x`-axis.