Triangles def and d'e'f' are shown on the coordinate plane below: . triangle def and triangle d prime e prime f prime with ordered pairs at d negative 1, 6, at e 1, 3, at f 6, 3, at d prime 1, negative 6, at e prime negative 1, negative 3, at f prime negative 6, negative 3. . what rotation was applied to triangle def to create triangle d'e'f'? . a.90° clockwise. b.180°. c. none of the above. d.90° counterclockwise

The correct answer is:
180° rotation.

Explanation:
Comparing the points D, E and F to D', E' and F', we see that the x- and y-coordinates of each have been negated, but they are still in the same position in the ordered pair.

 A 90° rotation counterclockwise will take coordinates (x, y) and map them to (-y, x), negating the y-coordinate and swapping the x- and y-coordinates.

 A 90° rotation clockwise will map coordinates (x, y) to (y, -x), negating the x-coordinate and swapping the x- and y-coordinates.

Performing either of these would leave our image with a coordinate that needs negated, as well as needing to swap the coordinates back around. 

This means we would have to perform the same rotation again; if we began with 90° clockwise, we would rotate 90 degrees clockwise again; if we began with 90° counter-clockwise, we would rotate 90 degrees counterclockwise again. Either way this rotates the figure a total of 180° and gives us the desired coordinates.

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