A triangle has corners at $(3, 8 )$ , ( 5, -2) $, and$ ( 1, -1)#. If the triangle is reflected across the x-axis, what will its new centroid be?

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Answer 1 · 2016-05-14T12:50:26

Coordinates of centroid will be $(3,-5/3)$

The centroid of a triangle whose vertices are $(x_1,y_1)$ , (x_2,y_2) $and (x_3,y_3)$ is given by

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

Hence centrid of given triangle is $((3+5+1)/3,(8+(-2)+(-1))/3)$ or $(3,5/3)$ .

Now, when a point $(x,y)$ is reflected across the $x$ -axis, its coordinates become $(x,-y)$ and hence

New coordinates are $(3,-8)$ , $(5,2)$ and $(1,1)$ and even
coordinates of centroid will have same rule.

Coordinates of centroid will be $(3,-5/3)$

A triangle has corners at (3, 8 )(3, 8 ), ( 5, -2), and , and ( 1, -1)#. If the triangle is reflected across the x-axis, what will its new centroid be?