Question

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

Answer 1

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.

Answer 2

The Real answer is 90 degrees clockwise not 180 degrees, i tried the approved answer above and got it wrong. If you examine the picture it makes more sense than just rotating it 180 degrees, plus the question doesn't specify if it is 180 degrees clockwise, or counterclockwise, so it makes sense for the answer to be: 90 degrees clockwise!