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

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

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Answer 1 · 2016-04-19T09:30:00

Coordinates of new centroid are $(\frac{17}{3}, \frac{1}{3})$ $(17/3,1/3)$

Explanation:

Reflection of a point $(x, y)$ $(x,y)$ in $x$ $x$ -axis is $(x, - y)$ $(x,-y)$ .

Hence reflection of a triangle having corners at $(7, 2)$ $(7,2)$ , $(9, - 7)$ $(9,-7)$ and $(1, 4)$ $(1,4)$ will be a triangle with corners at $(7, - 2)$ $(7,-2)$ , $(9, 7)$ $(9,7)$ and $(1, - 4)$ $(1,-4)$ .

As coordinates of centroid of a triangle with points at $(x_{1}, y_{1})$ $(x_1,y_1)$ , $(x_{2}, y_{2})$ $(x_2,y_2)$ and $(x_{3}, y_{3})$ $(x_3,y_3)$ is $(\frac{x_{1} + x_{2} + x_{3}}{3}, \frac{y_{1} + y_{2} + y_{3}}{3})$ $((x_1+x_2+x_3)/3,(y_1+y_2+y_3)/3)$ and hence

coordinates of new centroid are $(\frac{7 + 9 + 1}{3}, \frac{- 2 + 7 - 4}{3})$ $((7+9+1)/3,(-2+7-4)/3)$ or $(\frac{17}{3}, \frac{1}{3})$ $(17/3,1/3)$

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

1 Answer

Explanation:

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Science

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