Question

A triangle has corners at `(6, 4 )`, ( 5, -3)`, and`( 2, -5)#. If the triangle is reflected across the x-axis, what will its new centroid be?

Answer 1

`(13/3,4/3)`

Explanation:

To begin with we require to find the coordinates of the existing centroid. This is just the average of the x and y-coordinates of the 3 vertices.

`rArrx_C=1/3(6+5+2)=13/3`

and `y_C=1/3(4-3-5)=-4/3`

`rArr"coordinates of centroid" =(13/3,-4/3)`

`color(blue)"Under a reflection in the x-axis"`

a point (x ,y) → (x ,-y)

`rArr(13/3,-4/3)to(13/3,4/3)" is the new centroid"`