Question

A triangle has corners at `(3, 8 )`, ( 5, -2)`, and`( 1, -1)#. If the triangle is reflected across the x-axis, what will its new centroid be?

Answer 1

Coordinates of centroid will be `(3,-5/3)`

Explanation:

The centroid of a triangle whose vertices are `(x_1,y_1)`, (x_2,y_2)`and (x_3,y_3)` is given by

`((x_1+x_2+x_3)/3,(y_1+y_2+y_3)/3)`

Hence centrid of given triangle is `((3+5+1)/3,(8+(-2)+(-1))/3)` or `(3,5/3)`.

Now, when a point `(x,y)` is reflected across the `x`-axis, its coordinates become `(x,-y)` and hence

New coordinates are `(3,-8)`, `(5,2)` and `(1,1)` and even
coordinates of centroid will have same rule.

Coordinates of centroid will be `(3,-5/3)`