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

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

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Answer 1 · 2016-04-20T10:20:05

Coordinates of new centroid are $(\frac{7}{3}, 0)$ $(7/3,0)$

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 $(2, 7)$ $(2,7)$ , $(5, - 2)$ $(5,-2)$ and $(1, - 5)$ $(1,-5)$ will be a triangle with corners at $(2, - 7)$ $(2,-7)$ , $(5, 2)$ $(5,2)$ and $(1, 5)$ $(1,5)$ .

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 $(\frac{2 + 5 + 1}{3}, \frac{- 7 + 2 + 5}{3})$ $((2+5+1)/3,(-7+2+5)/3)$ or $(\frac{7}{3}, 0)$ $(7/3,0)$

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