Let's first graph the polygon ABC with the given vertices.
A rotation is a transformation about a fixed point called the center of rotation. Each point of the original figure and its image are the same distance from the center of rotation. When a clockwise rotation is performed about the origin, the coordinates of the image can be written in relation to the coordinates of the preimage.
We want to rotate a triangle 90^(∘) counterclockwise about the origin. A rotation by 90^(∘) counterclockwise ends up in the same place as a rotation by 270^(∘) clockwise. Therefore, we can use the coordinate changes shown in the table that correspond to a 270^(∘) clockwise to determine the coordinates of the image of each vertex.
ccc
Preimage & & Image
(x,y) & → & (- y, x) [0.5em]
A(- 3,- 1) & & A'(1,- 3) [0.5em]
B(2,2) & & B'(- 2,2) [0.5em]
C(3,- 3) & & C'(3,3)
We can now plot the obtained points and draw the image of the given triangle after the rotation!
