Question

A triangle has corners at `(1, 5 )`, ( 6, 8)`, and`( 4, 2)#. If the triangle is reflected across the x-axis, what will its new centroid be?

Answer 1

Coordinates of new centroid`(color(blue)(11/3), color(red)(-5))`

Explanation:

Centroid coordinates

`x = (x_1 + x_2 + x_3)/3 = (1 + 6 + 4) / 3 =color(blue)( 11/3)`

`y = (y_1 + y_2 + y_3)/3 = (5 + 8 + 2) / 3 = color (blue)(5)`

Coordinates of centroid `color(blue)(11/3), color(blue )(5)`

Since the triangle is reflected across x-axis,
x coordinate of new centroid will remain the same. Only y coordinate will mirror and equidistant from the x-axis.

Coordinates of new centroid`(color(blue)(11/3), color(red)(-5))`