A triangle has corners at $(4, 3)$ $(4, 3 )$ , ( 7, -8) $, and$ $, and$ (6, -2 )#. If the triangle is reflected across the x-axis, what will its new centroid be?

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Answer 1 · 2016-05-25T09:10:42

New centroid is $(\frac{17}{3}, \frac{7}{3})$ $(17/3,7/3)$

The centroid of the triangle with corners at $(4, 3)$ $(4,3)$ , $(7, - 8)$ $(7,-8)$ and $(6, - 2)$ $(6, -2 )$ is

$(\frac{4 + 7 + 6}{3}, \frac{3 + (- 8) + (- 2)}{3})$ $((4+7+6)/3,(3+(-8)+(-2))/3)$ or $(\frac{17}{3}, - \frac{7}{3})$ $(17/3,-7/3)$

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 $(\frac{17}{3}, \frac{7}{3})$ $(17/3,7/3)$

A triangle has corners at (4, 3 )(4,3)(4, 3 ), ( 7, -8), and ,and, and (6, -2 )#. If the triangle is reflected across the x-axis, what will its new centroid be?