A triangle has corners at (3, 8 )(3,8), ( 2, -2), and ,and( 2, -1)#. If the triangle is reflected across the x-axis, what will its new centroid be?

1 Answer
Jim G.
Mar 13, 2016

(7/3 , -5/3 ) (73,−53)

Explanation:

First step is to find the coordinates of the centroid

Given the 3 vertices of a triangle (x_1,y_1),(x_2,y_2),(x_3,y_3)(x1,y1),(x2,y2),(x3,y3)

x-coord of centroid = 1/3(x_1+x_2+x_3)=13(x1+x2+x3)

and y-coord of centroid = 1/3(y_1+y_2+y_3)=13(y1+y2+y3)

here let(x_1,y_1)=(3,8) , (x_2,y_2)=(2,-2). (x_3,y_3)=(2,-1)(x1,y1)=(3,8),(x2,y2)=(2,−2).(x3,y3)=(2,−1)

hence coords of centroid = [1/3(3+2+2),1/3(8-2-1)] = (7/3,5/3)=[13(3+2+2),13(8−2−1)]=(73,53)

Now under reflection in the x-axis a point (x,y) → (x,-y)

new centroid : (7/3,5/3) → (7/3,-5/3) (73,53)→(73,−53)

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