Question

Triangles def and d²e²f² 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 negative 6, negative 1, at e prime negative 3, 1, at f prime negative 3, 6. What rotation was applied to triangle def to create triangle d²e²f²?

1) 90°Counterclockwise
2) 90°Clockwise
3) none of the above
4) 180°

Answer 1

The rotation applied to triangle DEF to create triangle D²E²F² involves swapping the x and y coordinates and flipping the sign of the new y-coordinate, which indicates a 90° clockwise rotation and a reflection, not a standard rotation alone.

Step-by-step explanation:

To determine what rotation was applied to triangle DEF to create triangle D²E²F², we need to analyze the coordinates given for each corresponding point.

• Point D is at (-1, 6) and D² is at (-6, -1). If we rotate point D 90° counterclockwise about the origin, D would move to (-6, 1), which is not the coordinate of D².
• If we rotate point D 90° clockwise about the origin, D would move to (6, 1), which again does not match the coordinate of D².
• If we rotate point D 180°, it would move to (1, -6), which is also not correct.

However, if we look at the rotation patterns for each point, we notice that the x and y coordinates are swapped and the sign of the new y-coordinate is flipped. This indicates a 90° clockwise rotation about the origin as per the standard counterclockwise cartesian plane rotation rules but with an added reflection across the x-axis due to the sign change in the y-coordinate. This is not a conventional rotation alone, so the correct answer is none of the above because it includes both rotation and reflection.