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 negative 4 right parenthesis

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

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

(−8,4)

Answer 1

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

For a point (x, y), after a 90° counterclockwise rotation, the new coordinates (x', y') are given by:
- \( x' = -y \)
- \( y' = x \)

Let's denote the original coordinates of point D as \( (x, y) \). We need those coordinates to apply the rotation formula. However, since the specific coordinates of point D are not provided in your question, I can't calculate D' directly without that information.

If you provide the coordinates of point D, I could apply the transformation and give you the correct answer. Alternatively, if you already know the coordinates of D and can check the results against the options you listed, you can determine which response is correct.

Here’s a summary of how to analyze any point based on what you find: substitute the \( (x, y) \) values into the rules to find \( D' \) and compare it with the options given below:

1. (8, −4)
2. (4, −8)
3. (8, 4)
4. (−8, 4)

Please provide the coordinates of point D for further assistance!