Let's start by graphing the given coordinates so that we can see the polygon.
When a figure is rotated 180^(∘) counterclockwise about the origin, the coordinates of the vertices of the preimage will change in the following way.
(a,b)→ (- a, - b)
Using this rule and the vertices of the polygon, we can find the x- and y-coordinates of the vertices of the image.
(a,b)
(- a, - b)
A(4,2)
A'(- 4,- 2)
B(2,8)
B'(- 2,- 8)
C(8,0)
C'(- 8,0)
Knowing the vertices of â–³ A'B'C', we can draw the image.
