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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 8 comma 4 right parenthesis (−8,4) left parenthesis negative 8 comma 4 right parenthesis (8,−4) left parenthesis 8 comma negative 4 right parenthesis (4,−8) left parenthesis 4 comma negative 8 right parenthesis Skip to navigation

3 answers

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

If a point has coordinates (x, y), after a 90° counterclockwise rotation, the new coordinates (x', y') will be:

\[ (x', y') = (-y, x) \]

If we assume point D has coordinates (x, y), we apply the transformation:

  1. Replace x with -y
  2. Replace y with x

Once you know the original coordinates of point D, apply this transformation to find the coordinates of D'.

However, since I don't have the original coordinates from your description, I cannot give you the exact coordinates of D'. Please provide the coordinates of point D, and I can help you calculate D' after the rotation!

To determine the new coordinates \( D' \) after a 90° counterclockwise rotation about the origin, you'll use the coordinate transformation:

\[ (x', y') = (-y, x) \]

Let's evaluate each of your provided options based on the standard rotation effects:

  1. If D is at (x, y):
    • \( D' = (-y, x) \)

Now let's analyze the given coordinate options based solely on the transformation:

  • If \( D \) was at (8, 4):

    • \( D' = (-4, 8) \)

  • If \( D \) was at (-8, 4):

    • \( D' = (-4, -8) \)

  • If \( D \) was at (8, -4):

    • \( D' = (4, 8) \)

  • If \( D \) was at (4, -8):

    • \( D' = (8, 4) \)

Now based on the options provided in your question, we need to identify which of those options matches with these calculations.

Given Options

  1. (8, 4)
  2. (-8, 4)
  3. (8, -4)
  4. (4, -8)

Conclusion

None of the options appear to match correctly the result of a 90° counterclockwise rotation transformation without knowing the original coordinates.

To provide a definitive answer, please confirm the original coordinates of point D, and based on that, I can guide you to the correct answer or verify which among your options corresponds to the transformation. If these are the only options, and we continue with my calculations based on hinted operations, the correct new coordinates from an assumed D transformation can suggest potential answers.

Could you provide the original D coordinate for certainty?