Question

A triangle has corners at `(6, 3 )`, ( 8, -2)`, and`(1, -1 )#. If the triangle is reflected across the x-axis, what will its new centroid be?

Answer 1

(5 ,0)

Explanation:

The first step here is to find the coordinates of the centroid of the triangle.

Given the 3 vertices of a triangle `(x_1,y_1),(x_2,y_2),(x_3,y_3)`

Then the centroid is calculated as follows:

`color(red)(|bar(ul(color(white)(a/a)color(black)(x_c=1/3(x_1+x_2+x_3), y_c=1/3(y_1+y_2+y_3))color(white)(a/a)|)))`

let `(x_1,y_1)=(6,3),(x_2,y_2)=(8,-2),(x_3,y_3)=(1,-1)`

`rArrx_c=1/3(6+8+1)" and " y_c=1/3(3-2-1)`

coordinates of centroid = (5 ,0)

Under a reflection in the x-axis

A point (x ,y) → (x ,-y)

Since the point (5 ,0) is on the x-axis, it's position will remain the same under a reflection in the x-axis.

hence (5 ,0) → (5 ,0)