A triangle has corners at $(3, 7)$ $(3, 7 )$ , ( 5, -5) $, and$ $, and$ ( 2, -1)#. If the triangle is reflected across the x-axis, what will its new centroid be?

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Answer 1 · 2016-05-25T09:05:15

New centroid is $(\frac{10}{3}, - \frac{1}{3})$ $(10/3,-1/3)$

The centroid of the triangle with corners at $(3, 7)$ $(3,7)$ , $(5, - 5)$ $(5,-5)$ and $(2, - 1)$ $(2, -1 )$ is

$(\frac{3 + 5 + 2}{3}, \frac{7 + (- 5) + (- 1)}{3})$ $((3+5+2)/3,(7+(-5)+(-1))/3)$ or $(\frac{10}{3}, \frac{1}{3})$ $(10/3,1/3)$

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 $(\frac{10}{3}, - \frac{1}{3})$ $(10/3,-1/3)$

A triangle has corners at (3,7)(3, 7 ), ( 5, -5),and, and ( 2, -1)#. If the triangle is reflected across the x-axis, what will its new centroid be?