A figure is rotated 90 degrees counterclockwise about the origin. Which of the following function mappings was applied? Enter the number of the correct option. Option #1: (x,y)→(y,−x) Option #2: (x,y)→(−y,x) Option #3: (x,y)→(−x,−y) Option #4: (x,y)→(y,x) (1 point) The mapping for a 90-degree counterclockwise rotation is Option #
The correct option for a 90-degree counterclockwise rotation about the origin is Option #2: (x, y) → (-y, x).
1: (x,y)→(y,−x)
The correct option for a 90-degree counterclockwise rotation about the origin is Option #2: (x, y) → (-y, x).
To understand why, let's break it down step by step.
In a counterclockwise rotation, the point (x, y) moves to a new position in the coordinate plane. During a 90-degree counterclockwise rotation, the y-coordinate becomes the new x-coordinate and the x-coordinate becomes the new y-coordinate.
Additionally, to rotate counterclockwise about the origin, the sign of the new x-coordinate is flipped.
So, the mapping (x, y) → (-y, x) satisfies both conditions: the y-coordinate becomes the new x-coordinate, the x-coordinate becomes the new y-coordinate, and the x-coordinate is negated.
Therefore, the correct option is Option #2: (x, y) → (-y, x).