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?

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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?

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Answer 1 · 2016-05-18T09:40:26

$(3, \frac{5}{3})$ $(3,5/3)$

Explanation:

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

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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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Impact of this question

Science

Math

Humanities

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