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.
ccc
Preimage & & Image
(x,y) & → & (- x, - y) [0.5em]
F(1,2) & & F'(- 1, - 2) [0.5em]
G(3,5) & & G'(- 3, - 5) [0.5em]
H(3,2) & & H'(- 3,- 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 △ FGH 180^(∘) clockwise about the origin so that we can see how it is mapped onto △ F'G'H'.
