A triangle has corners at $(1, 3 )$ , ( 8, -4) $, and$ (1, -5 )#. If the triangle is reflected across the x-axis, what will its new centroid be?

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Answer 1 · 2016-03-20T06:44:38

New centroid will be $(10/3,2)$ .

When a point $(x,y)$ is reflected across $x$ -axis, new point becomes $(x,-y)$ .

Hence corners of new triangle will be $(1,-3)$ , $(8,4)$ and $(1,5)$ .

As centroid of a triangle with sides $(x_1,y_1)$ , $(x_2,y_2)$ and $(x_3,y_3)$ is given by $((x_1+x_2+x_3)/3,(y_1+y_2+y_3)/3)$

New centroid will be $((1+8+1)/3,(-3+4+5)/3)$ or $(10/3,2)$ .

A triangle has corners at (1, 3 )(1, 3 ), ( 8, -4), and , and (1, -5 )#. If the triangle is reflected across the x-axis, what will its new centroid be?