A triangle has corners at $(1, 2)$ $(1, 2 )$ , ( 1 , -9) $, and$ $, and$ ( 7, -1)#. If the triangle is reflected across the x-axis, what will its new centroid be?

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Answer 1 · 2016-03-11T16:58:55

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

The centroid of the triangle with corners at $(1, 2)$ $(1,2)$ , $(1, - 9)$ $(1,-9)$ and $(7, - 1)$ $(7, -1 )$ is

$(\frac{1 + 1 + 7}{3}, \frac{2 + (- 9) + (- 1)}{3})$ $((1+1+7)/3,(2+(-9)+(-1))/3)$ or $(3, - \frac{8}{3})$ $(3,-8/3)$

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 $(3, \frac{8}{3})$ $(3,8/3)$

A triangle has corners at (1,2)(1, 2 ), ( 1 , -9),and, and ( 7, -1)#. If the triangle is reflected across the x-axis, what will its new centroid be?