A triangle has corners at $(8, 1)$ $(8, 1 )$ , ( 5, -8) $, and$ $, and$ (7, -2 )#. If the triangle is reflected across the x-axis, what will its new centroid be?

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A triangle has corners at $(8, 1)$ $(8, 1 )$ , ( 5, -8) $, and$ $, and$ (7, -2 )#. If the triangle is reflected across the x-axis, what will its new centroid be?

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Answer 1 · 2016-12-06T03:11:26

The coordinates of the centroid of the triangle after it has been reflected over the $x$ $x$ axis are $(\frac{20}{3}, 3)$ $(20/3,3)$ .

Explanation:

The reflection of $(x, y)$ $(x,y)$ over the $x$ $x$ axis is $(x, - y)$ $(x, -y)$ .

If a triangle has vertices of $(8, 1), (5, - 8), (7, - 2)$ $(8,1), (5,-8), (7,-2)$ ,

the vertices after reflecting it over the $x$ $x$ axis are $(8, - 1), (5, 8), (7, 2)$ $(8,-1), (5,8), (7,2)$ .

To find the coordinates of a centroid of a triangle with vertices at $(x_{1}, y_{1}), (x_{2}, y_{2}), (x_{3}, y_{3})$ $(x_1, y_1), (x_2,y_2), (x_3,y_3)$ , use the formula

${(x, y)}_{centroid} = (\frac{x_{1} + x_{2} + x_{3}}{3}, \frac{y_{1} + y_{2} + y_{3}}{3})$ $(x,y)_"centroid"= ((x_1+x_2+x_3)/3, (y_1+y_2+y_3)/3)$

${(x, y)}_{centroid} = (\frac{8 + 5 + 7}{3}, \frac{- 1 + 8 + 2}{3}) = (\frac{20}{3}, 3)$ $(x,y)_"centroid"=((8+5+7)/3, (-1+8+2)/3)=(20/3,3)$

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A triangle has corners at $(8, 1)$ $(8, 1 )$ , ( 5, -8) $, and$ $, and$ (7, -2 )#. If the triangle is reflected across the x-axis, what will its new centroid be?

1 Answer

Explanation:

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A triangle has corners at (8,1)(8, 1 ), ( 5, -8),and, and (7, -2 )#. If the triangle is reflected across the x-axis, what will its new centroid be?

1 Answer

Explanation:

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A triangle has corners at $(8, 1)$ $(8, 1 )$ , ( 5, -8) $, and$ $, and$ (7, -2 )#. If the triangle is reflected across the x-axis, what will its new centroid be?