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 180^(∘) 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 (x,y)
Image (- x, - y)
Simplify
F(- 2,1)
F(-(- 2),-1)
F'(2, - 1)
G(- 1,3)
G(-(- 1),- 3)
G'(1, - 3)
H(3,1)
H(- 3,- 1)
H'(- 3,- 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 FGH 180^(∘) clockwise about the origin so that we can see how it is mapped onto F'G'H'.
