A triangle has corners at $(6, 3)$ $(6, 3 )$ , ( 8, -7) $, and$ $, and$ (1, -1 )#. If the triangle is reflected across the x-axis, what will its new centroid be?

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Answer 1 · 2016-05-25T09:02:07

New centroid is $(5, \frac{5}{3})$ $(5,5/3)$

The centroid of the triangle with corners at $(6, 3)$ $(6,3)$ , $(8, - 7)$ $(8,-7)$ and $(1, - 1)$ $(1, -1 )$ is

$(\frac{6 + 8 + 1}{3}, \frac{3 + (- 7) + (- 1)}{3})$ $((6+8+1)/3,(3+(-7)+(-1))/3)$ or $(5, - \frac{5}{3})$ $(5,-5/3)$

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 $(5, \frac{5}{3})$ $(5,5/3)$

A triangle has corners at (6,3)(6, 3 ), ( 8, -7),and, and (1, -1 )#. If the triangle is reflected across the x-axis, what will its new centroid be?