A triangle has corners at $(3, 2)$ $(3, 2 )$ , ( 3, 1) $, and$ $, and$ ( 4, 3)#. If the triangle is reflected across the x-axis, what will its new centroid be?

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Answer 1 · 2016-05-25T09:12:39

New centroid is $(\frac{10}{3}, - 2)$ $(10/3,-2)$

The centroid of the triangle with corners at $(3, 2)$ $(3,2)$ , $(3, 1)$ $(3,1)$ and $(4, 3)$ $(4, 3)$ is

$(\frac{3 + 3 + 4}{3}, \frac{2 + 1 + 3}{3})$ $((3+3+4)/3,(2+1+3)/3)$ or $(\frac{10}{3}, 2)$ $(10/3,2)$

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 $(\frac{10}{3}, - 2)$ $(10/3,-2)$

A triangle has corners at (3,2)(3, 2 ), ( 3, 1),and, and ( 4, 3)#. If the triangle is reflected across the x-axis, what will its new centroid be?