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]
J(-4,1) & & J'(1,4) [0.5em]
K(-2, 1) & & K'(1,2) [0.5em]
L(-4,- 3) & & L'(- 3,4)
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 △ JKL 90^(∘) clockwise about the origin so that we can see how it is mapped onto △ J'K'L'.
