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

(4,−8)
left parenthesis 4 comma negative 8 right parenthesis

(−8,4)
left parenthesis negative 8 comma 4 right parenthesis

(8,4)
left parenthesis 8 comma 4 right parenthesis

(8,−4)

Answer 1

To perform a 90° counterclockwise rotation about the origin on a point \((x, y)\), the new coordinates \((x', y')\) can be calculated using the following transformation:

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

Let's denote the coordinates of point D as \((x, y)\). Unfortunately, I cannot see the image you're referring to and thus do not know the coordinates of point D.

However, you can apply the transformation to the coordinates of point D.

1. Take the original coordinates of point D, say \((x, y)\).
2. Substitute these values into the transformation to find the new coordinates.

For example, if the coordinates of D are \((4, 8)\): \[ D' = (-8, 4) \]

You would then select the matching response from the provided options.

If you provide the coordinates of point D, I can help you calculate D' specifically.

Answer 2

D is on -4x -8y