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 negative 4 right parenthesis

(8,4)

Answer 1

To find the coordinates of D' after a 90° counterclockwise rotation about the origin, you can use the rotation transformation rules for points in the coordinate plane.

If a point has coordinates \((x, y)\), after a 90° counterclockwise rotation, its new coordinates will be \((-y, x)\).

Now, apply this transformation to point D, whose coordinates you should know from the original quadrilateral in the image.

For example, if D is at the coordinates \((4, -8)\):

1. Identify \(x\) and \(y\):

   • \(x = 4\)
   • \(y = -8\)

2. Apply the rotation:

   • The new \(x\) will be \(-(-8) = 8\)
   • The new \(y\) will be \(4\)

Thus, the new coordinates D' will be \((8, 4)\).

Check the options:

• \((4, -8)\)
• \((-8, 4)\)
• \((8, -4)\)
• \((8, 4)\)

The correct response is: (8, 4).