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. with Pre Image D (-4, -8)

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 negative 4 right parenthesis

(8,4)
left parenthesis 8 comma 4 right parenthesis
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Answer 1

To perform a 90° counterclockwise rotation about the origin, you can use the following transformation on the coordinates (x, y):

\[ (x, y) \rightarrow (-y, x) \]

For the point D (-4, -8):

1. Identify the coordinates: \(x = -4\) and \(y = -8\).
2. Apply the transformation:

\[ D' = (-(-8), -4) = (8, -4) \]

Thus, the coordinates of D' after a 90° counterclockwise rotation are (8, -4).

Therefore, the correct response is:

(8, -4)