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A triangle has corners at #(4, 4 )#, ( 3, -2)#, and #( 5, -3)#. If the triangle is reflected across the x-axis, what will its new centroid be?

Answer 1

Wyatt Anderson

#(4,1/3)#

#"the coordinates of the centroid are the average of the"# #"coordinates of the vertices"#

#"centroid "=(1/3(4+3+5),1/3(4-2-3))#

#color(white)("centroid ")=(4,-1/3)#

#"under a reflection in the x-axis"#

#• " a point "(x,y)to(x,-y)#

#rArr"new centroid "=(4,1/3)#

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Answer 2

Evelyn Arboleda

To find the centroid of the reflected triangle across the x-axis, we reflect each vertex across the x-axis and then find the average of the new coordinates to determine the centroid.

Original vertices: A(4, 4), B(3, -2), C(5, -3)

Reflected vertices: A'(4, -4), B'(3, 2), C'(5, 3)

Now, find the average of the x-coordinates and the y-coordinates of the reflected vertices to find the new centroid:

New centroid = ((4+3+5)/3, (-4+2+3)/3) = (4, 1/3)

Therefore, the new centroid of the reflected triangle across the x-axis is (4, 1/3).

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