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

1 Answer

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Answer 1 · 2017-02-11T21:22:48

$(11/3,-4/3)$

Explanation:

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

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

$rArrx_("centroid")=1/3(1+6+4)=11/3$

$rArry_("centroid")=1/3(2+7-5)=4/3$

$"coordinates of centroid "=(11/3,4/3)$

Under a reflection in the x-axis.

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

$rArr"new centroid "=(11/3,-4/3)$

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