Final answer:
The rotation applied to triangle DEF to create triangle D'E'F' is 90° counterclockwise (Option A).
Step-by-step explanation:
The question asks about the type of rotation applied to triangle DEF to arrive at the position of triangle D'E'F' on a coordinate plane. To determine the rotation, one can look at the orientation of the vertices and the sides of the triangles in relation to the coordinate system.
When a shape undergoes a 90° counterclockwise rotation, every point of the shape moves along a circular path and ends up on a position that is 90 degrees to the counterclockwise direction from its original position. If the shape were to rotate 90° clockwise instead, the points would end up on a circular path 90 degrees to the clockwise direction from the original position.
Comparing the orientation of sides and vertices of both triangles will reveal which rotation occurred. The original directions of the sides for triangle DEF compared to the rotated triangle D'E'F' will indicate if the directions correspond to a 90° counterclockwise or clockwise turn, or potentially none of the above options if the rotation doesn't align with standard 90° increments.
To determine the rotation that was applied to triangle DEF to create triangle D'E'F', we need to analyze the given information.
The statement 'They point in opposite directions' suggests that a 180° rotation was applied. Additionally, the statement 'They are perpendicular, forming a 270° angle between each other' indicates a 90° counterclockwise rotation. Based on this information, we can conclude that the rotation applied is 90° counterclockwise (Option A).