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^(∘) clockwise about the origin. 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(5,3) & & A'(3,- 5) [0.5em]
B(4,- 1) & & B'(-1,- 4) [0.5em]
C(1,- 1) & & C'(- 1,- 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 △ ABC 90^(∘) clockwise about the origin so that we can see how it is mapped onto △ A'B'C'.
