Question

A triangle has corners at `(6, 4 )`, ( 1, -2)`, and`( 4, -1)#. If the triangle is reflected across the x-axis, what will its new centroid be?

Answer 1

`(11/3,-1/3)`

Explanation:

The first step is to find the centroid of the given triangle.

If `(x_1,y_1),(x_2,y_2)" and " (x_3,y_3)` are the vertices of a triangle,
Then
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x-coordinate of centroid `=1/3(x_1+x_2+x_3)`
and y-coordinate of centroid `=1/3(y_1+y_2+y_3)`
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here the coordinates of the vertices are (6 ,4), (1 ,-2) and (4 ,-1)

x-coordinate `=1/3(6+1+4)=11/3`

and y-coordinate `=1/3(4-2-1)=1/3`

hence coordinates of centroid `=(11/3,1/3)`

• Under a reflection in the x-axis

a point (x ,y) → (x ,-y)

hence 'new' centroid `=(11/3,-1/3)`