A rotation is a transformation about a fixed point called 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. 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]
P(- 3,2) & & P'(- 2,- 3) [0.5em]
Q(6,1) & & Q'(- 1, 6) [0.5em]
R(- 1,- 5) & & R'(5,- 1)
We can now plot the obtained points and draw the image of the given triangle after the rotation!
Extra
Visualizing the Rotation
Let's rotate △ PQR 90^(∘) counterclockwise about the origin so that we can see how it is mapped onto △ P'Q'R'.
