1 answer

A triangle has corners at #(6, 3 )#, ( 8, -2)#, and #(1, -1 )#. If the triangle is reflected

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?

Answers

(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)

.

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