Rotations Quick Check 4 of 54 of 5 Items Question Use the image to answer the 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 negative 8 comma 4 right parenthesis (4,−8) left parenthesis 4 comma negative 8 right parenthesis (8,4) left parenthesis 8 comma 4 right parenthesis (8,−4) left parenthesis 8 comma negative 4 right parenthesis Skip to navigation page 16 of 16 Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.

Answer 1

To find the coordinates of a point after a 90° counterclockwise rotation about the origin, you can use the following transformation rule:

If a point has coordinates (x, y), then after a 90° counterclockwise rotation, the new coordinates (x', y') will be: \[ (x', y') = (-y, x) \]

So, if you start with the point \( D (x, y) \), you will calculate:

1. Negate the y-coordinate: \( x' = -y \)
2. Take the x-coordinate as the new y-coordinate: \( y' = x \)

If you have the coordinates of point D, plug those values into the above transformation rule to find the coordinates of D′ after the rotation.

Since the image is not provided here, please check the original coordinates of point D (x, y), apply the transformation, and then select the correct response based on the calculated result. If you provide the coordinates of point D, I can assist further in finding D′.