Question

A figure is rotated 90 degrees counterclockwise about the origin. Which of the following function mappings was applied? (1 point)

(xy)-(y-x)

(x,y)(y, x)

(x,y)(x,y)

(x,y)(y,-x)

Answer 1

When a point \((x, y)\) is rotated 90 degrees counterclockwise about the origin, the coordinates transform according to the following mapping:

\[
(x, y) \to (-y, x)
\]

However, none of the options you provided directly match this. Let's evaluate the given options to see which one resembles the transformation:

1. \((xy) - (y-x)\) - This option doesn't represent a mapping of points in a coordinate system.
2. \((x, y) \to (y, x)\) - This is a switch of the x and y coordinates (reflection over the line y=x), not a rotation.
3. \((x, y) \to (x, y)\) - This keeps the point unchanged, which is not a rotation.
4. \((x, y) \to (y, -x)\) - This option closely resembles a 90-degree counterclockwise rotation, but is actually the mapping for a 90-degree clockwise rotation.

Therefore, evaluating the transformations, it appears none correctly describe a 90-degree counterclockwise rotation. However, please double-check if the structure has changed in terms of placement, as the closest indicated is following the format of transformation before correction. As described \((x, y) \to (-y, x)\) fits the expected trajectory.

Make sure to refer back to the original instructions given that you need a function from the provided set or structure if there are any updates or corrections needed in the specified notation.