A triangle has corners at $(8, 3)$ $(8, 3 )$ , ( 5, -8) $, and$ $, and$ (7, -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 $(8, 3)$ $(8, 3 )$ , ( 5, -8) $, and$ $, and$ (7, -4 )#. If the triangle is reflected across the x-axis, what will its new centroid be?

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Answer 1 · 2016-10-23T13:08:19

$(\frac{20}{3}, 3)$ $(20/3,3)$

Explanation:

The first step is to find the coordinates of the centroid, $(x_{c}, y_{c})$ $(x_c,y_c)$

Given that the vertices of a triangle are $(x_{1}, y_{1}), (x_{2}, y_{2}), (x_{3}, y_{3})$ $(x_1,y_1),(x_2,y_2),(x_3,y_3)$

Then.

$x_{c} = \frac{1}{3} (x_{1} + x_{2} + x_{3}) the average of the x-coordinates$ $x_c=1/3(x_1+x_2+x_3)" the average of the x-coordinates"$

and $y_{c} = \frac{1}{3} (y_{1} + y_{2} + y_{3}) the average of the y-coordinates$ $y_c=1/3(y_1+y_2+y_3)" the average of the y-coordinates"$

Here.

$(x_{1}, y_{1}) = (8, 3), (x_{2}, y_{2}) = (5, - 8), (x_{3}, y_{3}) = (7, - 4)$ $(x_1,y_1)=(8,3),(x_2,y_2)=(5,-8), (x_3,y_3)=(7,-4)$

$\Rightarrow x_{c} = \frac{1}{3} (8 + 5 + 7) = \frac{20}{3}$ $rArrx_c=1/3(8+5+7)=20/3$

and $y_{c} = \frac{1}{3} (3 - 8 - 4) = - 3$ $y_c=1/3(3-8-4)=-3$

coordinates of centroid $= (\frac{20}{3}, - 3)$ $=(20/3,-3)$

Under reflection in the x-axis, a point (x ,y) → (x ,-y)

$\Rightarrow (\frac{20}{3}, - 3) \to (\frac{20}{3}, 3)$ $rArr(20/3,-3)to(20/3,3)$

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A triangle has corners at $(8, 3)$ $(8, 3 )$ , ( 5, -8) $, and$ $, and$ (7, -4 )#. If the triangle is reflected across the x-axis, what will its new centroid be?

1 Answer

Explanation:

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Impact of this question

Science

Math

Humanities

... and beyond

A triangle has corners at (8,3)(8, 3 ), ( 5, -8),and, and (7, -4 )#. If the triangle is reflected across the x-axis, what will its new centroid be?

1 Answer

Explanation:

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Impact of this question

A triangle has corners at $(8, 3)$ $(8, 3 )$ , ( 5, -8) $, and$ $, and$ (7, -4 )#. If the triangle is reflected across the x-axis, what will its new centroid be?