A triangle has corners at $(3, 7 )$ , ( 5, 1) $, and$ ( 6, 3)#. If the triangle is reflected across the x-axis, what will its new centroid be?

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Answer 1 · 2018-06-04T11:30:40

$color(blue)((14/3,-11/3)$

First we need to find the centroid. The centroid can be found by finding the arithmetic mean of the $x$ and $y$ coordinates:

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

Using given points:

$((3+5+6)/3,(7+1+3)/3)=>(14/3,11/3)$

Let $C=(14/3,11/3)$

A reflection in the line $y=0$ ( x axis ) maps:

$(x,y)->(x,-y)$

Therefore:

$C->C'=(14/3,11/3)->(14/3,-11/3)$

A triangle has corners at (3, 7 )(3, 7 ), ( 5, 1), and , and ( 6, 3)#. If the triangle is reflected across the x-axis, what will its new centroid be?