A triangle has corners at $(4, 8)$ $(4, 8 )$ , ( 9, -2) $, and$ $, and$ ( 2, -1)#. If the triangle is reflected across the x-axis, what will its new centroid be?

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Answer 1 · 2016-06-14T20:10:38

$(5, - \frac{5}{3}) .$ $(5,-5/3).$

The centroid of the given triangle is $(\frac{4 + 9 + 2}{3}, \frac{8 - 2 - 1}{3}) = (5, \frac{5}{3}) .$ $((4+9+2)/3, (8-2-1)/3) = (5,5/3).$

Now, a pt. $(a, b)$ $(a,b)$ is reflected in X-axis, its reflection will be the pt. $(a, - b)$ $(a,-b)$ .

Hence, new co-ordinates of the reflected centroid will be $(5, - \frac{5}{3}) .$ $(5,-5/3).$

A triangle has corners at (4, 8 )(4,8)(4, 8 ), ( 9, -2), and ,and, and ( 2, -1)#. If the triangle is reflected across the x-axis, what will its new centroid be?