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

Jan 16, 2016

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

#### Explanation:

• 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:
$\text{Centroid (C)} = \left(\frac{{x}_{1} + {x}_{2} + {x}_{3}}{3} , \frac{{y}_{1} + {y}_{2} + {y}_{3}}{3}\right)$ (TutorVista.com, 2016)

• $C = \left(\frac{0 + 1 + 7}{3} , \frac{5 - 2 - 4}{3}\right)$

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

• The reflection of that centroid is $\left(2 \frac{2}{3} , \frac{1}{3}\right)$

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