A triangle has corners at $(0, 5 )$ , ( 1, -6) $, and$ (8, -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 $(0, 5 )$ , ( 1, -6) $, and$ (8, -4 )#. If the triangle is reflected across the x-axis, what will its new centroid be?

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Answer 1 · 2016-05-18T09:40:26

$(3,5/3)$

Explanation:

The centroid $C$ also known as barycenter, of a triangle with vertex given as ${a,b,c}$ is calculated as:
$C = (a+b+c)/3$ . Our triangle has $a = (0,5), b= (1,-6), c = (8,-4)$ so
we have $C = (3,-5/3)$ . Reflecting the triangle across the $x$ axis
implies in reflecting also the barycenter. Choosing the $x$ axis facilitate calculations because the $C$ point perpendicular projection over the $x$ axis is exactly its $x$ component with $y = 0$ . Call this projected point $C_x = (3,0)$ . The reflected point is calculated as $C_r =C + 2 (C_x-C) = (3,5/3)$

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A triangle has corners at $(0, 5 )$ , ( 1, -6) $, and$ (8, -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 (0, 5 )(0, 5 ), ( 1, -6), and , and (8, -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 $(0, 5 )$ , ( 1, -6) $, and$ (8, -4 )#. If the triangle is reflected across the x-axis, what will its new centroid be?