Question

Imagine a 90° (counterclockwise) rotation about the origin of the figure in the image. Select the coordinate of D′ . (1 point) Responses (8,4) left parenthesis 8 comma 4 right parenthesis (4,−8) left parenthesis 4 comma negative 8 right parenthesis (−8,4) left parenthesis negative 8 comma 4 right parenthesis (8,−4)

Answer 1

To find the coordinates of point D' after a 90° counterclockwise rotation about the origin, we can use the following transformation formula for a point (x, y):

- After a 90° counterclockwise rotation, the new coordinates (x', y') become (-y, x).

Given the options, we need to apply this transformation.

Assuming D has coordinates (x, y), after a 90° counterclockwise rotation, it becomes (-y, x).

Now, let's check the given options:

1. **(8, 4)**: This would mean the original point was (4, 8). Rotating gives (-8, 4) (but this is not an option).
2. **(4, −8)**: This would mean the original point was (-8, 4). Rotating gives (4, -8) (not this).
3. **(−8, 4)**: This would mean the original point was (4, -8). Rotating gives (-(-8), 4) = (8, 4) (but this is not an option).
4. **(8, −4)**: This would mean the original point was (−4, 8). Rotating gives (4, 8) (not this).

It seems you've provided multiple choices. The actual D and its coordinates should be clarified. However, from what was analyzed, if we don't know the original point, the option that might represent D′ (after rotation) could typically be calculated directly if D's original coordinates were known.

If D were at (x, y), the rotation transformation is consistent with (-y, x). Please provide the original coordinates for a more accurate determination or provide D's original location so the transformation can be directly assessed.