A triangle has corners at $(3, 9)$ $(3, 9 )$ , ( 6, -5) $, and$ $, and$ ( 4, -9 )#. If the triangle is reflected across the x-axis, what will its new centroid be?

Question

What equation results when the function $f (x) = 3^{x}$ $f(x) = 3^(x)$ is reflected in the x-axis and translated...
A triangle has corners at $(7, 1)$ $(7, 1 )$ , ( 3 , 2) $, and$ $, and$ ( 8 , 5 )#. What will the new...
A triangle has corners at $(2, 1)$ $(2, 1 )$ , ( -4 , 3) $, and$ $, and$ ( 8 , 5 )#. What will the new...
A triangle has corners at $(2, 1)$ $(2, 1 )$ , ( -4 , 3) $, and$ $, and$ ( 1 , -2)#. What will the new...
A triangle has corners at $(2, 1)$ $(2, 1 )$ , ( 6 , 1) $, and$ $, and$ ( 1 , -2)#. What will the new...
A triangle has corners at $(2, - 5)$ $(2, -5 )$ , ( 6 , 1) $, and$ $, and$ ( 1 , -2)#. What will the new...
A triangle has corners at $(2, - 5)$ $(2, -5 )$ , ( 6 , 1) $, and$ $, and$ ( 4 , 3)#. What will the new...
A triangle has corners at $(3, - 5)$ $(3, -5 )$ , ( 2 , -1) $, and$ $, and$ ( 4 , 3)#. What will the new...
A triangle has corners at $(2, - 7)$ $(2, -7 )$ , ( 1 , -3) $, and$ $, and$ ( 4 , 3)#. What will the new...
A triangle has corners at $(4, 6)$ $(4, 6 )$ , ( 1 , -3) $, and$ $, and$ ( 1 , -4)#. What will the new...

2000 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-05-25T09:00:00

New centroid is $(\frac{13}{3}, \frac{5}{3})$ $(13/3,5/3)$

The centroid of the triangle with corners at $(3, 9)$ $(3,9)$ , $(6, - 5)$ $(6,-5)$ and $(4, - 9)$ $(4, -9 )$ is

$(\frac{3 + 6 + 4}{3}, \frac{9 + (- 5) + (- 9)}{3})$ $((3+6+4)/3,(9+(-5)+(-9))/3)$ or $(\frac{13}{3}, - \frac{5}{3})$ $(13/3,-5/3)$

When triangle is reflected across the x-axis, its centroid too is reflected across the x-axis

and as reflection of a point $(x_{1}, y_{1})$ $(x_1,y_1)$ in x-axis is $(x_{1}, - y_{1})$ $(x_1,-y_1)$ ,

New centroid is $(\frac{13}{3}, \frac{5}{3})$ $(13/3,5/3)$

A triangle has corners at (3,9)(3, 9 ), ( 6, -5),and, and ( 4, -9 )#. If the triangle is reflected across the x-axis, what will its new centroid be?