A triangle has corners at $(4, 3 )$ , ( 7, -4) $, and$ (6, -5 )#. If the triangle is reflected across the x-axis, what will its new centroid be?

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Answer 1 · 2016-03-01T10:15:50

Centroid will be at $(17/3,2)$

Centroid of a triangle, whose vertices are $(x_1,y_1)$ , $(x_2,y_2)$ and $(x_3,y_3)$ is $((x_1+x_2+x_3)/3, (y_1+y_2+y_3)/3)$ .

When a point $(x,y)$ is reflected in $x$ axis, coordinated of reflection point are $(x,-y)$ .

Hence coordinates of corners of triangle $(4,3)$ , $(7,-4)$ and $(6,-5)$ on reflection become $(4,-3)$ , $(7,4)$ and $(6,5)$ .

Centroid of reflected triangle will be

$((4+7+6)/3, (-3+4+5)/3)$ or $(17/3,2)$

A triangle has corners at (4, 3 )(4, 3 ), ( 7, -4), and , and (6, -5 )#. If the triangle is reflected across the x-axis, what will its new centroid be?