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

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

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

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

To determine the coordinates of point D' after a 90° counterclockwise rotation about the origin, we can apply the following transformation rule for rotation:

A point (x, y) will transform to (-y, x) after a 90° counterclockwise rotation.

Now, let's apply this to the point D.

Assuming point D had coordinates (x, y), after the rotation, the new coordinates (D′) would be:

• D′ = (-y, x)

Since the options provided do not specify the original coordinates of point D, let's analyze the choices given, assuming potential original points (x, y):

1. If D = (8, 4) → D' = (-4, 8)
2. If D = (4, -8) → D' = (8, 4)
3. If D = (8, -4) → D' = (4, 8)
4. If D = (-8, 4) → D' = (-4, -8)

Reviewing the responses provided, the transformed point corresponding to a standard coordinate transformation would not match any of the given options.

However, if we are working from an unknown point, we only need to understand the transformation.

Taking (4, -8):

• After rotation:
• (-(-8), 4) = (8, 4)

Therefore, the coordinates of point D' that correspond to point D given in the options would stand as (4, -8) after effect of transformation.