Use the image to answer the question.

Question

A quadrilateral is plotted on a coordinate plane with both the axes ranging from negative 10 to 10.

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
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Answer 1

To perform a 90° counterclockwise rotation of a point \((x, y)\) around the origin, the new coordinates \((x', y')\) are given by the formula:

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

You need to apply this transformation to the coordinates of point D. However, since I don't have access to the image to find the coordinates of point D, I can show you how to apply the formula:

If you can find the coordinates of point D \((x, y)\) from the image:

1. Substitute \(y\) for \(-x'\) and \(x\) for \(y'\).
2. This will give you the new coordinates after a 90° counterclockwise rotation.

For example, if point D has coordinates \((2, 3)\):

• After the rotation, the coordinates would be: \[ (-3, 2) \]

Once you find the coordinates of D and apply the formula, you can match your result with one of the provided options:

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

Please provide the coordinates of point D from the image so I can help you find the correct answer.