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. Therefore, we can use the information in the above table to find the coordinates of the image of each vertex.
Preimage& & &Image
(x , y)& → & &(y, - x)
A(0 , - 4)& → & A'&(- 4, 0)
B(0 , - 1)& → & B'&(- 1, 0)
C(2 , - 1)& → & C'&(- 1, - 2)
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'.
