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

Question

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

2009 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-04-20T10:20:05

Coordinates of new centroid are $(7/3,0)$

Reflection of a point $(x,y)$ in $x$ -axis is $(x,-y)$ .

Hence reflection of a triangle having corners at $(2,7)$ , $(5,-2)$ and $(1,-5)$ will be a triangle with corners at $(2,-7)$ , $(5,2)$ and $(1,5)$ .

As coordinates of centroid of a triangle with points at $(x_1,y_1)$ , $(x_2,y_2)$ and $(x_3,y_3)$ is $((x_1+x_2+x_3)/3,(y_1+y_2+y_3)/3)$ and hence

Coordinates of new centroid are $((2+5+1)/3,(-7+2+5)/3)$ or $(7/3,0)$

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