A triangle has corners at $(6, 5)$ $(6, 5 )$ , ( 3, -6) $, and$ $, and$ (8, -1 )#. If the triangle is reflected across the x-axis, what will its new centroid be?

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A triangle has corners at $(6, 5)$ $(6, 5 )$ , ( 3, -6) $, and$ $, and$ (8, -1 )#. If the triangle is reflected across the x-axis, what will its new centroid be?

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Answer 1 · 2016-03-28T06:40:46

The new centroid is at $(\frac{17}{3}, \frac{2}{3})$ $(17/3, 2/3)$

Explanation:

The old centroid is at
$x_{c} = \frac{x_{1} + x_{2} + x_{3}}{3} = \frac{6 + 3 + 8}{3} = \frac{17}{3}$ $x_c=(x_1+x_2+x_3)/3=(6+3+8)/3=17/3$

$y_{c} = \frac{y_{1} + y_{2} + y_{3}}{3} = \frac{5 - 6 - 1}{3} = - \frac{2}{3}$ $y_c=(y_1+y_2+y_3)/3=(5-6-1)/3=-2/3$

The old centroid is at $(\frac{17}{3}, - \frac{2}{3})$ $(17/3, -2/3)$

Since, we are reflecting the triangle across the x-axis, the abscissa of the centroid will not change. Only the ordinate will change. So the new centroid will be at $(\frac{17}{3}, \frac{2}{3})$ $(17/3, 2/3)$

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A triangle has corners at $(6, 5)$ $(6, 5 )$ , ( 3, -6) $, and$ $, and$ (8, -1 )#. 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 (6,5)(6, 5 ), ( 3, -6),and, and (8, -1 )#. If the triangle is reflected across the x-axis, what will its new centroid be?

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A triangle has corners at $(6, 5)$ $(6, 5 )$ , ( 3, -6) $, and$ $, and$ (8, -1 )#. If the triangle is reflected across the x-axis, what will its new centroid be?