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 quadrilateral 180^(∘) 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) & → & (- x, - y) [0.5em]
J(- 4,- 4) & & J'(4,4) [0.5em]
K(- 4,2) & & K'(4,- 2) [0.5em]
L(- 1,0) & & L'(1,0) [0.5em]
M(- 2,- 3) & & M'(2,3)
We can now plot the obtained points and draw the image of the given quadrilateral after the rotation!
Extra
Visualizing the Rotation
Let's rotate JKLM 180^(∘) clockwise about the origin so that we can see how it is mapped onto J'K'L'M'.
