Question

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

Answer 1

`(7/3 , -5/3 )`

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)`

x-coord of centroid `= 1/3(x_1+x_2+x_3)`

and y-coord of centroid `= 1/3(y_1+y_2+y_3)`

here let`(x_1,y_1)=(3,8) , (x_2,y_2)=(2,-2). (x_3,y_3)=(2,-1)`

hence coords of centroid`= [1/3(3+2+2),1/3(8-2-1)] = (7/3,5/3)`

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

new centroid : `(7/3,5/3) → (7/3,-5/3)`