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 270^(∘) clockwise about the origin. Therefore, we can use the information in the above table to find the coordinates of the image of each vertex.
ccc
Preimage & & Image
(x,y) & → & (- y,x) [0.5em]
A(- 4,2) & & A'(- 2,- 4) [0.5em]
B(- 2,2) & & B'(- 2,- 2) [0.5em]
C(- 3,4) & & C'(- 4, - 3)
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 △ ABC 270^(∘) clockwise about the origin so that we can see how it is mapped onto △ A'B'C'.
