A triangle has corners at $(1, 2)$ $(1, 2 )$ , ( 5, -9) $, and$ $, and$ ( 2, -1)#. If the triangle is reflected across the x-axis, what will its new centroid be?

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Answer 1 · 2016-03-11T09:55:31

New centroid is $(\frac{8}{3}, \frac{8}{3})$ $(8/3,8/3)$

The centroid of the triangle with corners at $(1, 2)$ $(1,2)$ , $(5, - 9)$ $(5,-9)$ and $(2, - 1)$ $(2, -1 )$ is

$(\frac{1 + 5 + 2}{3}, \frac{2 + (- 9) + (- 1)}{3})$ $((1+5+2)/3,(2+(-9)+(-1))/3)$ or $(\frac{8}{3}, - \frac{8}{3})$ $(8/3,-8/3)$

When triangle is reflected across the x-axis, its centroid too is reflected across the x-axis

and as reflection of a point $(x_{1}, y_{1})$ $(x_1,y_1)$ in x-axis is $(x_{1}, - y_{1})$ $(x_1,-y_1)$ ,

new centroid is $(\frac{8}{3}, \frac{8}{3})$ $(8/3,8/3)$

A triangle has corners at (1,2)(1, 2 ), ( 5, -9),and, and ( 2, -1)#. If the triangle is reflected across the x-axis, what will its new centroid be?