A triangle has corners at $(0, 5)$ $(0, 5 )$ , ( 1, -2) $, and$ $, and$ (7, -4 )#. If the triangle is reflected across the x-axis, what will its new centroid be?

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Answer 1 · 2016-01-16T19:47:22

$C = (2 \frac{2}{3}, - \frac{1}{3})$ $C=(2 2/3,-1/3)$

You can find the centroid of the triangle before it is reflected, and just reflect that point.
When you reflect a point across the x axis, you change the sign of the y-coordinate and leave the x-coordinate as it is.
You can find the centroid you can use the centroid formula:
$Centroid (C) = (\frac{x_{1} + x_{2} + x_{3}}{3}, \frac{y_{1} + y_{2} + y_{3}}{3})$ $"Centroid (C)"=((x_1+x_2+x_3)/3,(y_1+y_2+y_3)/3)$ (TutorVista.com, 2016)
$C = (\frac{0 + 1 + 7}{3}, \frac{5 - 2 - 4}{3})$ $C=((0+1+7)/3,(5-2-4)/3)$

$C = (2 \frac{2}{3}, - \frac{1}{3})$ $C=(2 2/3,-1/3)$

-References
TutorVista.com, 2016. Centroid Formula. [Online]. Available from:
http://formulas.tutorvista.com/math/centroid-formula.html. [Accessed: 16th Jan 2016].

A triangle has corners at (0, 5 )(0,5)(0, 5 ), ( 1, -2), and ,and, and (7, -4 )#. If the triangle is reflected across the x-axis, what will its new centroid be?