A triangle has corners at $(6, 7)$ $(6, 7 )$ , ( 2, -4) $, and$ $, and$ (9, -1 )#. If the triangle is reflected across the x-axis, what will its new centroid be?

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Answer 1 · 2016-03-11T09:52:27

New centroid is $(\frac{17}{3}, - \frac{2}{3})$ $(17/3,-2/3)$

The centroid of the triangle with corners at $(6, 7)$ $(6,7)$ , $(2, - 4)$ $( 2,-4)$ and $(9, - 1)$ $(9, -1 )$ is

$(\frac{6 + 2 + 9}{3}, \frac{7 + (- 4) + (- 1)}{3})$ $((6+2+9)/3,(7+(-4)+(-1))/3)$ or $(\frac{17}{3}, \frac{2}{3})$ $(17/3,2/3)$

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 $(\frac{17}{3}, - \frac{2}{3})$ $(17/3,-2/3)$

A triangle has corners at (6,7)(6, 7 ), ( 2, -4),and, and (9, -1 )#. If the triangle is reflected across the x-axis, what will its new centroid be?