A triangle has corners at $(1, 2)$ $(1, 2 )$ , ( 6, 7) $, and$ $, and$ ( 4, -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 $(1, 2)$ $(1, 2 )$ , ( 6, 7) $, and$ $, and$ ( 4, -5)#. If the triangle is reflected across the x-axis, what will its new centroid be?

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Answer 1 · 2017-02-11T21:22:48

$(\frac{11}{3}, - \frac{4}{3})$ $(11/3,-4/3)$

Explanation:

Before we can find the 'new' centroid we must find the existing one.

The coordinates of the centroid are the $average$ $color(blue)"average"$ of the x and y coordinates of the 3 vertices.

$\Rightarrow x_{centroid} = \frac{1}{3} (1 + 6 + 4) = \frac{11}{3}$ $rArrx_("centroid")=1/3(1+6+4)=11/3$

$\Rightarrow y_{centroid} = \frac{1}{3} (2 + 7 - 5) = \frac{4}{3}$ $rArry_("centroid")=1/3(2+7-5)=4/3$

$coordinates of centroid = (\frac{11}{3}, \frac{4}{3})$ $"coordinates of centroid "=(11/3,4/3)$

Under a reflection in the x-axis.

$a point (x, y) \to (x, - y)$ $"a point "(x,y)to(x,-y)$

$\Rightarrow new centroid = (\frac{11}{3}, - \frac{4}{3})$ $rArr"new centroid "=(11/3,-4/3)$

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A triangle has corners at $(1, 2)$ $(1, 2 )$ , ( 6, 7) $, and$ $, and$ ( 4, -5)#. 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 (1,2)(1, 2 ), ( 6, 7),and, and ( 4, -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 $(1, 2)$ $(1, 2 )$ , ( 6, 7) $, and$ $, and$ ( 4, -5)#. If the triangle is reflected across the x-axis, what will its new centroid be?