A triangle has corners at $(3, 2)$ $(3, 2 )$ , ( 5, 7) $, and$ $, and$ ( 2, -5)#. If the triangle is reflected across the x-axis, what will its new centroid be?

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Answer 1 · 2016-05-25T08:54:33

New centroid is $(\frac{10}{3}, - \frac{4}{3})$ $(10/3,-4/3)$

The centroid of the triangle with corners at $(3, 2)$ $(3,2)$ , $(5, 7)$ $(5,7)$ and $(2, - 5)$ $(2, -5 )$ is

$(\frac{3 + 5 + 2}{3}, \frac{2 + 7 + (- 5)}{3})$ $((3+5+2)/3,(2+7+(-5))/3)$ or $(\frac{10}{3}, \frac{4}{3})$ $(10/3,4/3)$

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 $(\frac{10}{3}, - \frac{4}{3})$ $(10/3,-4/3)$

A triangle has corners at (3,2)(3, 2 ), ( 5, 7),and, and ( 2, -5)#. If the triangle is reflected across the x-axis, what will its new centroid be?