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^(∘) counterclockwise about the origin. A rotation by 90^(∘) counterclockwise ends up in the same place as a rotation by 270^(∘) clockwise. Therefore, we can use the coordinate changes shown in the table that correspond to a 270^(∘) clockwise to determine the coordinates of the image of each vertex.
ccc
Preimage & & Image
(x,y) & → & (- y, x) [0.5em]
A(- 4,6) & & A'(- 6,- 4) [0.5em]
B(- 6,1) & & B'(- 1,- 6) [0.5em]
C(- 2,1) & & C'(- 1,- 2)
We can now plot the obtained points and draw the image of the given triangle after the rotation!
Therefore, the correct option is D.
Extra
Visualizing the Rotation
Let's rotate △ ABC 90^(∘) counterclockwise about the origin so that we can see how it is mapped onto △ A'B'C'.
