A 180^(∘) rotation counterclockwise about the origin will change the coordinates of the vertices such that (a,b)→ (- a,- b).
Practice makes perfect
Let's start by looking at the given polygon. Examining the figure, we can see the coordinates of the vertices of the triangle.
D(- 3,- 1) E(- 1,2) F(4,- 2)
When a figure is rotated 180^(∘) counterclockwise about the origin, the coordinates of the image's vertices will change in the following way.
(a,b)→ (- a,- b)
Using this rule and the vertices of △ DEF, we can find the x- and y-coordinates of the image's vertices.
△ DEF
(a,b)
(- a,- b)
D
(- 3,- 1)
(3,1)
E
(- 1,2)
(1,- 2)
F
(4,- 2)
(- 4,2)
Knowing the vertices of △ D'E'F', we can draw the image.
