A triangle has corners at $(4, 3)$ $(4, 3 )$ , ( 7, -4) $, and$ $, and$ (6, -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 $(4, 3)$ $(4, 3 )$ , ( 7, -4) $, and$ $, and$ (6, -5 )#. If the triangle is reflected across the x-axis, what will its new centroid be?

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Answer 1 · 2016-03-01T10:15:50

Centroid will be at $(\frac{17}{3}, 2)$ $(17/3,2)$

Explanation:

Centroid of a triangle, whose vertices are $(x_{1}, y_{1})$ $(x_1,y_1)$ , $(x_{2}, y_{2})$ $(x_2,y_2)$ and $(x_{3}, y_{3})$ $(x_3,y_3)$ is $(\frac{x_{1} + x_{2} + x_{3}}{3}, \frac{y_{1} + y_{2} + y_{3}}{3})$ $((x_1+x_2+x_3)/3, (y_1+y_2+y_3)/3)$ .

When a point $(x, y)$ $(x,y)$ is reflected in $x$ $x$ axis, coordinated of reflection point are $(x, - y)$ $(x,-y)$ .

Hence coordinates of corners of triangle $(4, 3)$ $(4,3)$ , $(7, - 4)$ $(7,-4)$ and $(6, - 5)$ $(6,-5)$ on reflection become $(4, - 3)$ $(4,-3)$ , $(7, 4)$ $(7,4)$ and $(6, 5)$ $(6,5)$ .

Centroid of reflected triangle will be

$(\frac{4 + 7 + 6}{3}, \frac{- 3 + 4 + 5}{3})$ $((4+7+6)/3, (-3+4+5)/3)$ or $(\frac{17}{3}, 2)$ $(17/3,2)$

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A triangle has corners at $(4, 3)$ $(4, 3 )$ , ( 7, -4) $, and$ $, and$ (6, -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 (4,3)(4, 3 ), ( 7, -4),and, and (6, -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 $(4, 3)$ $(4, 3 )$ , ( 7, -4) $, and$ $, and$ (6, -5 )#. If the triangle is reflected across the x-axis, what will its new centroid be?