A triangle has corners at $(3, 9 )$ , ( 7, -2) $, and$ ( 5, -9 )#. If the triangle is reflected across the x-axis, what will its new centroid be?

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Answer 1 · 2017-07-28T07:53:44

The new coordinates of the centroid is $=(5,2/3)$

Let the corners of the triangle be $(x_1,y_1)$ , $(x_2,y_2)$ and $(x_3,y_3)$

The coordinates of the centroid are

$C=((x_1+x_2+x_3)/2,(y_1+y_2+y_3)/3)$

Here, we have $(3,9)$ , $(7,-2)$ , and $(5,-9)$

So,

The coordinates of the centroid are $C=((3+7+5)/3,(9-2-9)/3)=(15/3,-2/3)=(5,-2/3)$

The matrix of the reflection acrossthe x-axis is

$M=((1,0),(0,-1))$

Therefore,

The new coordinates of the centroid is

$((x),(y))=((1,0),(0,-1))((5),(-2/3))=((5),(2/3))$

A triangle has corners at (3, 9 )(3, 9 ), ( 7, -2), and , and ( 5, -9 )#. If the triangle is reflected across the x-axis, what will its new centroid be?